1876 lines
414 KiB
Plaintext
1876 lines
414 KiB
Plaintext
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"# CDS: Numerical Methods -- Final Assignment\n",
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"\n",
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"- See lecture notes and documentation on Brightspace for Python and Jupyter basics. If you are stuck, try to google or get in touch via Discord.\n",
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"\n",
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"- Solutions must be submitted <font color=red>**individually**</font> via the Jupyter Hub until <font color=red>**Monday, April 4th, 23:59**</font>.\n",
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"\n",
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"- Make sure you fill in any place that says `YOUR CODE HERE` or \"YOUR ANSWER HERE\".\n",
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"\n",
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"- Remember to document your source codes (docstrings, comments where necessary) and to write it as clear as possible.\n",
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"\n",
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"- Do not forget to fully annotate all of your plots.\n",
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"\n",
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"## Submission\n",
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"\n",
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"1. make sure everything runs as expected\n",
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"2. **restart the kernel** (in the menubar, select Kernel$\\rightarrow$Restart)\n",
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"3. **run all cells** (in the menubar, select Cell$\\rightarrow$Run All)\n",
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"4. Check all outputs (Out[\\*]) for errors and **resolve them if necessary**\n",
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"5. submit your solutions **in time (before the deadline)**"
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]
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},
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}
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"source": [
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"## Tight-Binding Propagation Method Module\n",
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"\n",
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"### Tight-Binding Theory\n",
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"\n",
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"Solid state theory aims to describe crystalline structures defined by periodic arrangements of atomic positions $\\vec{R}_i$ with $i= 1 \\dots n$. To model the electronic properties of such a structure, we can use the so-called tight-binding method. Here one assumes that the problem for a single atom described by the Hamiltonian $H_{at}(\\vec{r})$ has already been solved, so that the atomic wave functions $\\phi_m(\\vec{r})$ are known. The Hamiltonian of the crystalline structure is then constructed from these atomic Hamiltonians as follows \n",
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"\n",
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"\\begin{align*}\n",
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" H(\\vec{r}) = \\sum_{i} H_{at}(\\vec{r} - \\vec{R}_i) + \\Delta V(\\vec{r}),\n",
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"\\end{align*}\n",
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"\n",
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"where $\\Delta V(\\vec{r})$ describes the changes to the atomic potentials due to the periodic arrangement. Solutions to the time-dependent Schrödinger equation $\\psi_n(\\vec{r})$ can then be approximated by linear combinations of the atomic orbitals, i.e. \n",
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"\n",
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"\\begin{align*}\n",
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" \\psi_m(\\vec{r}) = \\sum_{i} \\, c_{i,m} \\, \\phi_m(\\vec{r}-\\vec{R}_i). \n",
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"\\end{align*}\n",
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"\n",
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"Thus, our task is to find the coefficients $c_{i,m}$, which are the eigenfunctions of the tight-binding Hamiltonian $H_{tb}$. In the basis of the atomic orbitals $H_{tb}$ is an $n \\times n$ matrix which describes the \"hopping\" of an electron from one atomic position to the other. In this description the electrons are assumed to be tightly bound to the atomic positions, hence the name of the approach. In summary, we have reduced our original problem $H(\\vec{r})$, described in a continuous space $\\vec{r}$, to a strongly discretized problem $H_{tb}$ in the space of lattice coordinates $\\vec{R}_i$.\n",
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"\n",
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"### Propagation Method\n",
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"\t\n",
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"While this reduction already helps a lot, full diagonalizations of the tight-binding matrix is still not feasible if we need to describe realistic structures with thousands of atoms. For this case we like to have a method which allows us to study the electronic properties, without the need of fully diagonalizing the tight-binding matrix. The tight-biding propagation method allows for exactly this. By analyzing the propagation of an initial electronic state through the crystalline structure we also have access to the full eigenspectrum of $H_{tb}$, without explicit diagonalization.\n",
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"\t\n",
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"### Your Goal\n",
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" \n",
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"In the following you will setup the tight-binding Hamiltonian for a one-dimensional chain of atoms and numerically study its properties using exact diagonalization. Then you will compare it to the results obtained using the tight-binding propagation method. You will need some of the algorithms which you have implemented in the weekly assignments before. Additionally, you will need to implement a few new algorithms, which we have discussed in the last lecture. In principle there will be no need to use Numpy or Scipy (except for Numpy's array handling and a few other exceptions). However, if you encounter any problems with your own implementations of specific functionalities, you can use the Numpy and Scipy alternatives. Therefore you should be able to perform all of the following tasks in any case.\n",
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"\n",
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"Let us start by importing the necessary packages."
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]
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},
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}
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},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"from matplotlib import pyplot as plt"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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}
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},
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"source": [
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"## Step 1: Crystal Lattice\n",
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"\n",
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"### Task 1.1 [3 points]\n",
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"\n",
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"In the following exercises the atomic positions of the 1D crystal lattice will be fixed to $\\vec{R}_i = x_i = i a$, with $i = 0 \\dots n-1$ and $a$ being the lattice constant.\n",
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"\n",
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"Write a simple Python function that takes the chain length $n$ as an argument and returns the atomic positions $x_i$. Set $a = 1$ for all the following exercises."
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]
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},
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"cell_type": "code",
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"execution_count": 2,
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"checksum": "bad6e1d563be71de711926b41649c875",
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"grade": true,
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"grade_id": "cell-65a97e8f9f981da1",
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"locked": false,
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"points": 3,
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"schema_version": 3,
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}
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},
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"outputs": [],
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"source": [
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"def atomic_positions(n, a=1):\n",
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" \"\"\"\n",
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" Creates an array of atomic position in a 1D crystal lattice\n",
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" for lattice constant a having default value a = 1.\n",
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" \n",
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" Args:\n",
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" n: number of atoms in the 1D lattice string\n",
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" a: numerical value for the lattice constant\n",
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"\n",
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" Returns:\n",
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" A 1D array of atomic positions.\n",
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" \"\"\"\n",
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" \n",
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" return np.arange(n)*a"
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]
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},
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"metadata": {
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"source": [
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"## Step 2: Atomic Basis Functions\n",
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"\n",
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"Our atomic basis functions will be Gaussians of the form\n",
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"$$\n",
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"\\large\n",
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"\\phi(x, \\mu, \\sigma) = \\frac{1}{\\pi^{1/4} \\sigma^{1/2}} e^{-\\frac{1}{2} \\left(\\frac{x-\\mu}{\\sigma}\\right)^2},\n",
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"$$\n",
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"\twhere $\\mu$ is their localization position and $\\sigma$ their broadenings. We also choose to have just one orbital per atom so that we can drop the index $m$ from now on. \n",
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"\t\n",
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"### Task 2.1 [4 points]\n",
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"Implement a Python function which calculates $\\phi(x, \\mu, \\sigma)$ for a whole array of arbitrary $x$, centered at given $\\mu$ with a given broadening $\\sigma$.\n",
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"\n",
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"Plot all the atomic basis functions for a chain with $n = 10$ atoms, using $\\sigma = 0.25$. I.e. plot $\\phi(x, x_i, \\sigma)$ vs $x$, for all atomic positions $x_i$ in the chain."
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]
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"data": {
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\n",
|
|
"text/plain": [
|
|
"<Figure size 432x288 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"def atomic_basis(x, mu, sigma):\n",
|
|
" \"\"\"\n",
|
|
" Calculates the atomic basis functions for the 1D chain of atoms.\n",
|
|
" \n",
|
|
" Args:\n",
|
|
" x: array of positions to calculate the wavefunction at\n",
|
|
" mu: atomic position(s) to center Gaussian wavefunction at\n",
|
|
" sigma: broadening constant for Gaussian function(s)\n",
|
|
"\n",
|
|
" Returns:\n",
|
|
" An array of values for the wavefunction over the positions\n",
|
|
" as given by x with shape len(x) by len(mu)\n",
|
|
" \"\"\"\n",
|
|
" \n",
|
|
" return np.pi**(-1/4)*sigma**(-1/2)*np.exp(-1/2*(np.subtract.outer(x, mu)/sigma)**2)\n",
|
|
"\n",
|
|
"n = 10\n",
|
|
"sigma = .25\n",
|
|
"x = np.linspace(-2, 12, 1000)\n",
|
|
"\n",
|
|
"plt.figure()\n",
|
|
"plt.xlabel(\"$x$\")\n",
|
|
"plt.ylabel(\"$\\phi$\")\n",
|
|
"\n",
|
|
"for mu in atomic_positions(n):\n",
|
|
" plt.plot(x, atomic_basis(x, mu, sigma), label=\"n = \" + str(mu))\n",
|
|
"\n",
|
|
"plt.legend()\n",
|
|
"plt.tight_layout()\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "e1c7774260f02916e34521c6236638f4",
|
|
"grade": false,
|
|
"grade_id": "cell-e5c9315357a401f9",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 2.2 [6 points]\n",
|
|
"Implement a Python function to calculate numerical integrals (using for example the composite trapezoid or Simpson rule). This one should be general enough to calculate integrals $\\int_a^b f(x) dx$ for arbitrary functions $f(x)$, as you will need it for other tasks as well.\n",
|
|
"\n",
|
|
"Implement a simple unit test for your integration function."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 4,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "aecc6d50a1ffd4e4bfbfe3573847edf8",
|
|
"grade": true,
|
|
"grade_id": "cell-d851197b213e5d2d",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def integrate(yk, x):\n",
|
|
" \"\"\"\n",
|
|
" Numerically integrates function yk over [x[0], x[-1]] using Simpson's 3/8\n",
|
|
" rule over the grid provided by x.\n",
|
|
" \n",
|
|
" Args:\n",
|
|
" yk: function of one numerical argument that returns a numeric\n",
|
|
" or an array of function values such that x[i] corresponds to yk[i]\n",
|
|
" x: array of numerics as argument to yk\n",
|
|
"\n",
|
|
" Returns:\n",
|
|
" A numeric value for the quadrature of yk over x with error\n",
|
|
" of order \n",
|
|
" \"\"\"\n",
|
|
" \n",
|
|
" # If yk is callable, we use it to determine the function values\n",
|
|
" # over array x.\n",
|
|
" if callable(yk):\n",
|
|
" yk = yk(x)\n",
|
|
" \n",
|
|
" # The distance h_i = x[i + 1] - x[i] is not necessarily constant. The choice of\n",
|
|
" # partitioning of the interval is subject to mathematical considerations I will\n",
|
|
" # not go into.\n",
|
|
" h = x[1:] - x[:-1]\n",
|
|
" \n",
|
|
" integral = 0\n",
|
|
" integral += 3/8*(x[1] - x[0])*yk[0]\n",
|
|
" integral += 9/8*h[1::3]@yk[1:-1:3]\n",
|
|
" integral += 9/8*h[2::3]@yk[2:-1:3]\n",
|
|
" integral += 6/8*h[ ::3]@yk[ :-1:3]\n",
|
|
" integral += 3/8*(x[-1] - x[-2])*yk[-1]\n",
|
|
" return integral"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 5,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "6ab06c87cf65c73463ed243e46d63b3d",
|
|
"grade": true,
|
|
"grade_id": "cell-59912b2862fbce5a",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def test_integrate():\n",
|
|
" # Test integral 1 of f with F its primitive with integration constant 0\n",
|
|
" f = lambda x: x**2\n",
|
|
" F = lambda x: x**3/3\n",
|
|
" x = np.logspace(0, 3, 1000000)\n",
|
|
" assert np.isclose(integrate(f, x), F(x[-1]) - F(x[0]))\n",
|
|
" \n",
|
|
" # Test integral 2 of f with F its primitive with integration constant 0\n",
|
|
" f = lambda x: np.sin(2*x)/(2 + np.cos(2*x))\n",
|
|
" F = lambda x: -.5*np.log(np.cos(2*x) + 2)\n",
|
|
" x = np.linspace(0, 10, 1000)\n",
|
|
" assert np.isclose(integrate(f, x), F(x[-1]) - F(x[0]))\n",
|
|
" \n",
|
|
"test_integrate()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "8c1413a8a11006398e962e8c803ae001",
|
|
"grade": false,
|
|
"grade_id": "cell-86005829da536b5b",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 2.3 [2 points]\n",
|
|
"Use your Python integration function to check the orthogonality of the Gaussian basis functions by verifying the following condition $$\\delta_{ij} = \\int_{-\\infty}^{+\\infty} \\phi(x, x_i, \\sigma) \\, \\phi(x, x_j, \\sigma) \\, dx,$$ where $\\delta_{ii} \\approx 1$ and $\\delta_{ij} \\approx 0$ for $\\sigma = 0.25$."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 6,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "4751becb5d3cb7663536a0624b3d9c54",
|
|
"grade": true,
|
|
"grade_id": "cell-8a6a8db84dcef484",
|
|
"locked": false,
|
|
"points": 2,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"delta_00 = 1.00000 (self)\n",
|
|
"delta_01 = 0.01832 (nearest neighbours)\n",
|
|
"delta_02 = 0.00000\n",
|
|
"delta_03 = 0.00000\n",
|
|
"delta_04 = 0.00000\n",
|
|
"delta_05 = 0.00000\n",
|
|
"delta_06 = 0.00000\n",
|
|
"delta_07 = 0.00000\n",
|
|
"delta_08 = 0.00000\n",
|
|
"delta_09 = 0.00000\n",
|
|
"delta_10 = 0.01832 (nearest neighbours)\n",
|
|
"delta_11 = 1.00000 (self)\n",
|
|
"delta_12 = 0.01832 (nearest neighbours)\n",
|
|
"delta_13 = 0.00000\n",
|
|
"delta_14 = 0.00000\n",
|
|
"delta_15 = 0.00000\n",
|
|
"delta_16 = 0.00000\n",
|
|
"delta_17 = 0.00000\n",
|
|
"delta_18 = 0.00000\n",
|
|
"delta_19 = 0.00000\n",
|
|
"delta_20 = 0.00000\n",
|
|
"delta_21 = 0.01832 (nearest neighbours)\n",
|
|
"delta_22 = 1.00000 (self)\n",
|
|
"delta_23 = 0.01832 (nearest neighbours)\n",
|
|
"delta_24 = 0.00000\n",
|
|
"delta_25 = 0.00000\n",
|
|
"delta_26 = 0.00000\n",
|
|
"delta_27 = 0.00000\n",
|
|
"delta_28 = 0.00000\n",
|
|
"delta_29 = 0.00000\n",
|
|
"delta_30 = 0.00000\n",
|
|
"delta_31 = 0.00000\n",
|
|
"delta_32 = 0.01832 (nearest neighbours)\n",
|
|
"delta_33 = 1.00000 (self)\n",
|
|
"delta_34 = 0.01832 (nearest neighbours)\n",
|
|
"delta_35 = 0.00000\n",
|
|
"delta_36 = 0.00000\n",
|
|
"delta_37 = 0.00000\n",
|
|
"delta_38 = 0.00000\n",
|
|
"delta_39 = 0.00000\n",
|
|
"delta_40 = 0.00000\n",
|
|
"delta_41 = 0.00000\n",
|
|
"delta_42 = 0.00000\n",
|
|
"delta_43 = 0.01832 (nearest neighbours)\n",
|
|
"delta_44 = 1.00000 (self)\n",
|
|
"delta_45 = 0.01832 (nearest neighbours)\n",
|
|
"delta_46 = 0.00000\n",
|
|
"delta_47 = 0.00000\n",
|
|
"delta_48 = 0.00000\n",
|
|
"delta_49 = 0.00000\n",
|
|
"delta_50 = 0.00000\n",
|
|
"delta_51 = 0.00000\n",
|
|
"delta_52 = 0.00000\n",
|
|
"delta_53 = 0.00000\n",
|
|
"delta_54 = 0.01832 (nearest neighbours)\n",
|
|
"delta_55 = 1.00000 (self)\n",
|
|
"delta_56 = 0.01832 (nearest neighbours)\n",
|
|
"delta_57 = 0.00000\n",
|
|
"delta_58 = 0.00000\n",
|
|
"delta_59 = 0.00000\n",
|
|
"delta_60 = 0.00000\n",
|
|
"delta_61 = 0.00000\n",
|
|
"delta_62 = 0.00000\n",
|
|
"delta_63 = 0.00000\n",
|
|
"delta_64 = 0.00000\n",
|
|
"delta_65 = 0.01832 (nearest neighbours)\n",
|
|
"delta_66 = 1.00000 (self)\n",
|
|
"delta_67 = 0.01832 (nearest neighbours)\n",
|
|
"delta_68 = 0.00000\n",
|
|
"delta_69 = 0.00000\n",
|
|
"delta_70 = 0.00000\n",
|
|
"delta_71 = 0.00000\n",
|
|
"delta_72 = 0.00000\n",
|
|
"delta_73 = 0.00000\n",
|
|
"delta_74 = 0.00000\n",
|
|
"delta_75 = 0.00000\n",
|
|
"delta_76 = 0.01832 (nearest neighbours)\n",
|
|
"delta_77 = 1.00000 (self)\n",
|
|
"delta_78 = 0.01832 (nearest neighbours)\n",
|
|
"delta_79 = 0.00000\n",
|
|
"delta_80 = 0.00000\n",
|
|
"delta_81 = 0.00000\n",
|
|
"delta_82 = 0.00000\n",
|
|
"delta_83 = 0.00000\n",
|
|
"delta_84 = 0.00000\n",
|
|
"delta_85 = 0.00000\n",
|
|
"delta_86 = 0.00000\n",
|
|
"delta_87 = 0.01832 (nearest neighbours)\n",
|
|
"delta_88 = 1.00000 (self)\n",
|
|
"delta_89 = 0.01832 (nearest neighbours)\n",
|
|
"delta_90 = 0.00000\n",
|
|
"delta_91 = 0.00000\n",
|
|
"delta_92 = 0.00000\n",
|
|
"delta_93 = 0.00000\n",
|
|
"delta_94 = 0.00000\n",
|
|
"delta_95 = 0.00000\n",
|
|
"delta_96 = 0.00000\n",
|
|
"delta_97 = 0.00000\n",
|
|
"delta_98 = 0.01832 (nearest neighbours)\n",
|
|
"delta_99 = 1.00000 (self)\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"n = 10\n",
|
|
"sigma = .25\n",
|
|
"\n",
|
|
"positions = atomic_positions(n)\n",
|
|
"infty = 10000\n",
|
|
"x = np.linspace(-infty, infty, 1000000)\n",
|
|
"\n",
|
|
"def ijlabel(i, j):\n",
|
|
" \"\"\"\n",
|
|
" Returns a string label describing the relation between two states in words,\n",
|
|
" if they are close enough.\n",
|
|
" \"\"\"\n",
|
|
" \n",
|
|
" if i == j:\n",
|
|
" return \" (self)\"\n",
|
|
" if abs(i - j) == 1:\n",
|
|
" return \" (nearest neighbours)\"\n",
|
|
" # Default:\n",
|
|
" return \"\"\n",
|
|
"\n",
|
|
"for i in range(n):\n",
|
|
" for j in range(n):\n",
|
|
" integrand = lambda x: atomic_basis(x, positions[i], sigma)*atomic_basis(x, positions[j], sigma)\n",
|
|
" print(\"delta_{}{} = {:.5f}{}\".format(i, j, integrate(integrand, x), ijlabel(i, j)))\n",
|
|
"\n",
|
|
"# Yann had output:\n",
|
|
"#delta_00 = 1.00000\n",
|
|
"#delta_01 = 0.01832\n",
|
|
"#delta_02 = 0.00000\n",
|
|
"#delta_34 = 0.01832\n",
|
|
"# Explanation: next neighbours migth have some overlap. Further away, no overlap at all."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "e9ccbed5ba3e6b844bcc6e326053d8da",
|
|
"grade": false,
|
|
"grade_id": "cell-3cba7034f4eac62f",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"## Step 3: Tight-Binding Hamiltonian\n",
|
|
"\n",
|
|
"The tight-binding Hamiltonian for our 1D chain should describe the hopping of an electron from all atomic positions to their nearest left and right neighbours (i.e. no long-range hopping). The resulting matrix representation in the basis of the discrete $x_i$ positions is therefore given as a tri-diagonal $n \\times n$ matrix of the form\n",
|
|
"\n",
|
|
"\\begin{align}\n",
|
|
" \\mathbf{H}_{tb} =\n",
|
|
" \\left( \\begin{array}{cccc}\n",
|
|
" 0 & t & & 0\\\\\n",
|
|
" t & \\ddots & \\ddots & \\\\\n",
|
|
" & \\ddots & \\ddots & t \\\\\n",
|
|
" 0 & & t & 0\n",
|
|
" \\end{array} \\right),\n",
|
|
"\\end{align}\n",
|
|
"\n",
|
|
"where $t = t_{i,i\\pm1}$ is the nearest-neighbour hopping matrix element. A hopping matrix element $t_{i,j}$ is a measure for the probability of an electron to hop from site $i$ to site $j$. They are defined as\n",
|
|
"\n",
|
|
"\\begin{align}\n",
|
|
" t_{i,j} = \\int_{-\\infty}^{+\\infty} \\phi(x, x_i, \\sigma) \\, \\Delta V(x) \\, \\phi(x, x_j, \\sigma) \\, dx,\n",
|
|
"\\end{align}\n",
|
|
"\n",
|
|
"with the potential fixed to\n",
|
|
"\n",
|
|
"\\begin{align}\n",
|
|
" \\Delta V(x) = \\sum_i \\frac{-1}{|x - x_i| + 0.001}.\n",
|
|
"\\end{align}\n",
|
|
"\n",
|
|
"### Task 3.1 [3 points]\n",
|
|
"Write a Python function to calculate $t_{i,j}$, using $\\sigma = 0.25$. The function should have as input the indices $i$ and $j$, and the chain length $n$. Verify that the long-range hoppings $t_{i,i\\pm2}$ and $t_{i,i\\pm3}$ are negligible compared to $t_{i,i\\pm1}$.\n",
|
|
"\n",
|
|
"Hint: use your integration function from task 2.2"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 7,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "260ae3c806429aee5900599c01cb65c6",
|
|
"grade": true,
|
|
"grade_id": "cell-0abfcd1aa9fad2fa",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def hopping(i, j, n, sigma=.25):\n",
|
|
" \"\"\"\n",
|
|
" Calculates hopping matrix elements t_ij for sigma = 0.25 in a 1D\n",
|
|
" chain of n atoms at distance a = 1 from eachother.\n",
|
|
" \n",
|
|
" Args:\n",
|
|
" i: origin site index\n",
|
|
" j: destination site index\n",
|
|
" n: number of atoms in the chain\n",
|
|
" sigma: standard deviation to the Gaussian wave functions\n",
|
|
"\n",
|
|
" Returns:\n",
|
|
" Hopping parameter t_ij.\n",
|
|
" \"\"\"\n",
|
|
" \n",
|
|
" positions = atomic_positions(n)\n",
|
|
" \n",
|
|
" # This 'infinity' is large enough, as the Gaussians decay quite quickly\n",
|
|
" # away from the atomic positions, which we already saw in the overlap\n",
|
|
" # above. In fact, 99.7% of all probability mass is under the integral\n",
|
|
" # for x radius of 3*sigma from the centers x_i.\n",
|
|
" h = 1e-5\n",
|
|
" x = np.arange(positions[0] - 10*sigma, positions[-1] - 10*sigma, h)\n",
|
|
" \n",
|
|
" def V(x):\n",
|
|
" ret = np.zeros(x.shape)\n",
|
|
" for x_i in positions:\n",
|
|
" ret += -1./(np.abs(x - x_i) + 0.001)\n",
|
|
" return ret\n",
|
|
" # Instead of using a loop, one could vectorize the problem further by calculating all sum\n",
|
|
" # terms as elements of a len(x) by len(positions) matrix and then summing along the rows.\n",
|
|
" # In testing I found that this was slower than using the loop, so I commented it out.\n",
|
|
" # This might be due to the large memory overhead O(len(x)*len(positions)), and the fact that\n",
|
|
" # the len(positions) iterations already do vectorized calculations on len(x) >> len(positions)\n",
|
|
" # numbers, making the theoretical speed gain only plausible at larger len(positions). \n",
|
|
" #V = lambda x: np.sum( -1/( np.abs(np.subtract.outer(x, positions)) + 0.001 ), axis=1 )\n",
|
|
" \n",
|
|
" integrand = lambda x: atomic_basis(x, positions[i], sigma)*V(x)*atomic_basis(x, positions[j], sigma)\n",
|
|
" return integrate(integrand, x)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 8,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "b1a56ecde33e723ff450defcf5dc2e74",
|
|
"grade": true,
|
|
"grade_id": "cell-ea36ee5a2b35154c",
|
|
"locked": false,
|
|
"points": 0,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"For i = 0 ...\n",
|
|
"\tt_{i,i+1} = -0.13849173441658025\n",
|
|
"\tt_{i,i+2} = -3.088088057066831e-06\n",
|
|
"\tt_{i,i+3} = -1.8833562200578063e-15\n",
|
|
"\n",
|
|
"For i = 1 ...\n",
|
|
"\tt_{i,i-1} = -0.13849173441658025\n",
|
|
"\tt_{i,i+1} = -0.14871538221422848\n",
|
|
"\tt_{i,i+2} = -3.1306987950404085e-06\n",
|
|
"\tt_{i,i+3} = -1.945630457066332e-15\n",
|
|
"\n",
|
|
"For i = 2 ...\n",
|
|
"\tt_{i,i-1} = -0.14871538221422848\n",
|
|
"\tt_{i,i+1} = -0.15363274031153992\n",
|
|
"\tt_{i,i-2} = -3.088088057066831e-06\n",
|
|
"\tt_{i,i+2} = -3.152251440766849e-06\n",
|
|
"\tt_{i,i+3} = -1.9763481552880358e-15\n",
|
|
"\n",
|
|
"For i = 3 ...\n",
|
|
"\tt_{i,i-1} = -0.15363274031153992\n",
|
|
"\tt_{i,i+1} = -0.1560583006931239\n",
|
|
"\tt_{i,i-2} = -3.1306987950404085e-06\n",
|
|
"\tt_{i,i+2} = -3.1616643825949025e-06\n",
|
|
"\tt_{i,i-3} = -1.8833562200578063e-15\n",
|
|
"\tt_{i,i+3} = -1.9857521228152284e-15\n",
|
|
"\n",
|
|
"For i = 4 ...\n",
|
|
"\tt_{i,i-1} = -0.1560583006931239\n",
|
|
"\tt_{i,i+1} = -0.15680086580653224\n",
|
|
"\tt_{i,i-2} = -3.1522514407668485e-06\n",
|
|
"\tt_{i,i+2} = -3.1616580341274714e-06\n",
|
|
"\tt_{i,i-3} = -1.945630457066332e-15\n",
|
|
"\tt_{i,i+3} = -1.9763479030784917e-15\n",
|
|
"\n",
|
|
"For i = 5 ...\n",
|
|
"\tt_{i,i-1} = -0.15680086580653224\n",
|
|
"\tt_{i,i+1} = -0.1560582807779115\n",
|
|
"\tt_{i,i-2} = -3.1616643825949025e-06\n",
|
|
"\tt_{i,i+2} = -3.1503943708763577e-06\n",
|
|
"\tt_{i,i-3} = -1.9763481552880358e-15\n",
|
|
"\tt_{i,i+3} = -9.75855063584149e-16\n",
|
|
"\n",
|
|
"For i = 6 ...\n",
|
|
"\tt_{i,i-1} = -0.15605828077791148\n",
|
|
"\tt_{i,i+1} = -0.07705640452986241\n",
|
|
"\tt_{i,i-2} = -3.1616580341274714e-06\n",
|
|
"\tt_{i,i+2} = -1.8615080260773555e-09\n",
|
|
"\tt_{i,i-3} = -1.985752122815229e-15\n",
|
|
"\tt_{i,i+3} = -1.2516261372405081e-23\n",
|
|
"\n",
|
|
"For i = 7 ...\n",
|
|
"\tt_{i,i-1} = -0.07705640452986241\n",
|
|
"\tt_{i,i+1} = -9.883210483852472e-10\n",
|
|
"\tt_{i,i-2} = -3.1503943708763577e-06\n",
|
|
"\tt_{i,i+2} = -8.453472394803474e-24\n",
|
|
"\tt_{i,i-3} = -1.9763479030784917e-15\n",
|
|
"\n",
|
|
"For i = 8 ...\n",
|
|
"\tt_{i,i-1} = -9.88321048385247e-10\n",
|
|
"\tt_{i,i+1} = -7.16787287550824e-31\n",
|
|
"\tt_{i,i-2} = -1.8615080260773555e-09\n",
|
|
"\tt_{i,i-3} = -9.75855063584149e-16\n",
|
|
"\n",
|
|
"For i = 9 ...\n",
|
|
"\tt_{i,i-1} = -7.16787287550824e-31\n",
|
|
"\tt_{i,i-2} = -8.453472394803472e-24\n",
|
|
"\tt_{i,i-3} = -1.2516261372405081e-23\n",
|
|
"\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"n = 10\n",
|
|
"\n",
|
|
"for i in range(n):\n",
|
|
" print(\"For i =\", i, \"...\")\n",
|
|
" for r in range(1, 4):\n",
|
|
" if i - r >= 0:\n",
|
|
" print(\"\\tt_{{i,i-{}}} = {}\".format(r, hopping(i, i - r, n)))\n",
|
|
" if i + r < n:\n",
|
|
" print(\"\\tt_{{i,i+{}}} = {}\".format(r, hopping(i, i + r, n)))\n",
|
|
" print()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "7d2c8f74993fe38c2c979376961f869a",
|
|
"grade": false,
|
|
"grade_id": "cell-8a0f18c44306ae00",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 3.2 [3 points]\n",
|
|
"Implement a diagonalization routine for tri-diagonal matrices which returns all eigenvalues, for example using the $QR$ decomposition (it is fine to use Numpy's $\\text{qr()}$). \n",
|
|
"\n",
|
|
"Hint: For tri-diagonal matrices with vanishing diagonal elements, the $QR$-decomposition-based diagonalization algorithm gets trapped. To get around this you could, for example, add a diagonal $1$ to your matrix, and later subtract $1$ from each eigenvalue."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 9,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "c20cbcce0a7df50b6ae7b90c7aa35721",
|
|
"grade": true,
|
|
"grade_id": "cell-9d4942b717eadeb2",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def QREig(T, eps=1e-6, k_max=10000):\n",
|
|
" \"\"\"\n",
|
|
" Follows the method of the QR decomposition based diagonalization routine\n",
|
|
" for tridiagonal matrices. The matrix T is diagonalized, resulting in\n",
|
|
" all diagonal elements being an eigenvalue.\n",
|
|
" \n",
|
|
" Args:\n",
|
|
" T: a tridiagonaliz matrix.\n",
|
|
" eps: the desired accuracy.\n",
|
|
" k_max: maximum number of iterations after which to cut off\n",
|
|
" \n",
|
|
" Returns:\n",
|
|
" A one dimensional array with the eigenvalues of the matrix T.\n",
|
|
" \"\"\"\n",
|
|
" \n",
|
|
" e = eps + 1\n",
|
|
" k = 0\n",
|
|
" while e > eps and k < k_max:\n",
|
|
" k += 1\n",
|
|
" Q, R = np.linalg.qr(T)\n",
|
|
" T = np.matmul(R,Q)\n",
|
|
" e = np.sum(np.abs(np.diag(T, k=1)))\n",
|
|
" return np.diag(T)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "19976946c5746804cb08c34f0bda50fc",
|
|
"grade": false,
|
|
"grade_id": "cell-2d8fb5c080951dd5",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 3.3 [3 points]\n",
|
|
"Implement a unit test for your diagonalization routine."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 10,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "d95777361c07514a97ff1458f26f4f44",
|
|
"grade": true,
|
|
"grade_id": "cell-001cb3c043c4e371",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def test_QREig():\n",
|
|
" # Test case one\n",
|
|
" T = np.array([\n",
|
|
" [1,4,0,0],\n",
|
|
" [3,4,1,0],\n",
|
|
" [0,2,3,4],\n",
|
|
" [0,0,1,3]\n",
|
|
" ])\n",
|
|
" # Eigenvalues are roots of λ^4 - 11*λ^3 + 25*λ^2 + 31*λ - 46.\n",
|
|
" eigenvalues_of_T = np.array([-1.45350244, 1., 4.65531023, 6.79819221])\n",
|
|
" assert np.allclose(np.sort(QREig(T)), eigenvalues_of_T)\n",
|
|
" \n",
|
|
" # Test case two\n",
|
|
" T = np.array([\n",
|
|
" [1,4,0,0],\n",
|
|
" [3,0,1,0],\n",
|
|
" [0,2,0,4],\n",
|
|
" [0,0,0,3]\n",
|
|
" ])\n",
|
|
" eigenvalues_of_T = np.sort(np.linalg.eig(T)[0])\n",
|
|
" assert np.allclose(np.sort(QREig(T)), eigenvalues_of_T)\n",
|
|
"\n",
|
|
"test_QREig()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "83df149b46d779a846f9de925342b681",
|
|
"grade": false,
|
|
"grade_id": "cell-85c89b0eb0930f2b",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 3.4 [4 points]\n",
|
|
"First, write a function that generates your tight-binding Hamiltonian $\\mathbf{H}_{tb}$, for a given chain length $n$. Use $t = t_{i,i\\pm1}$, as calculated in task 3.1. You can choose any $i$ near the center of the chain for the calculation of $t$, as the chain is (approximately) periodic.\n",
|
|
"\n",
|
|
"Second, use your diagonalization routine to calculate all the eigenvalues $E_m$, for a variety of $n=10,20,40,80,100$. Sort the resulting $E_m$ and plot them vs. $m$."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 11,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "a0779b496fd41a4664bb0cdd857c70fc",
|
|
"grade": true,
|
|
"grade_id": "cell-764cb41c37700042",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def TBHamiltonian(n, sigma=.25):\n",
|
|
" \"\"\"\n",
|
|
" Generates the tight-binding hamiltonian H_tb for given chain length n,\n",
|
|
" using the approximation of constant hopping parameter in a periodic\n",
|
|
" chain of atoms.\n",
|
|
" \n",
|
|
" Args:\n",
|
|
" n: number of atoms in the chain\n",
|
|
" sigma: standard deviation to the Gaussian wave functions\n",
|
|
"\n",
|
|
" Returns:\n",
|
|
" Tight-binding hamiltonian H_tb.\n",
|
|
" \"\"\"\n",
|
|
" \n",
|
|
" # TODO: Comment on the weird 20% differences in hopping parameters.\n",
|
|
" \n",
|
|
" i = n//2\n",
|
|
" t = hopping(i, i + 1, n, sigma)\n",
|
|
" H_tb = (np.eye(n, n, -1) + np.eye(n, n, 1))*t\n",
|
|
" \n",
|
|
" return H_tb"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 12,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "634e139137eead8808d1d8ccb793d5a5",
|
|
"grade": true,
|
|
"grade_id": "cell-39ada0528e69d2e5",
|
|
"locked": false,
|
|
"points": 1,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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\n",
|
|
"text/plain": [
|
|
"<Figure size 432x288 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"plt.figure()\n",
|
|
"\n",
|
|
"for n in [10, 20, 40, 80, 100]:\n",
|
|
" H_tb = TBHamiltonian(n)\n",
|
|
" # TODO: Decide whether to implement this + 1 - 1 trick here or in QREig above.\n",
|
|
" E_m = QREig(H_tb + np.eye(n)) - 1\n",
|
|
" plt.plot(np.arange(len(E_m)) + 1, np.sort(E_m), label=\"n = {}\".format(n))\n",
|
|
"\n",
|
|
"plt.legend()\n",
|
|
"plt.title(\"Energy eigenvalues of $H_{{tb}}$ for different chain lengths $n$\")\n",
|
|
"plt.xlabel(\"$m$\")\n",
|
|
"plt.ylabel(\"$E_m$\")\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "c2b46d2fef4b0c243103a5a6f1111e2d",
|
|
"grade": false,
|
|
"grade_id": "cell-b7c84b8c4ed4c1be",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 3.5 [3 points]\n",
|
|
"Implement a function to calculate the so-called density-of-states \n",
|
|
"\n",
|
|
"\\begin{align*}\n",
|
|
" \\rho(\\omega) = \\frac{1}{N} \\sum_i \\delta(\\omega - E_i),\n",
|
|
"\\end{align*}\n",
|
|
"\n",
|
|
"for a variable energy grid $\\omega$. Do this by approximating the $\\delta$-distribution with a Gaussian. In detail, you can use your atomic orbital function $\\delta(\\omega - E_i) \\approx \\phi(\\omega, E_i, \\sigma_\\rho)$. Calculate the normalization factor $N$ such that $\\int \\rho(\\omega) dw = 1$ is fulfilled.\n",
|
|
"\n",
|
|
"Your function should take as input the energy grid $\\omega$, the eigenenergies $E_i$ and the broadening $\\sigma_\\rho$."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 13,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "ca46cf0b09305fafb522fc0395d1e495",
|
|
"grade": true,
|
|
"grade_id": "cell-d7c225b7687b5a9c",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def getDOS_ED(w, Ei, sigma):\n",
|
|
" \"\"\"\n",
|
|
" Calculates the density-of-states (DOS) for energy grid w by\n",
|
|
" counting the occupation using a Gaussian approximation to the\n",
|
|
" delta function.\n",
|
|
" \n",
|
|
" Args:\n",
|
|
" w: grid of energies to calculate the DOS over\n",
|
|
" Ei: array of n eigenenergies for the system\n",
|
|
" sigma: standard deviation to the Gaussian\n",
|
|
"\n",
|
|
" Returns:\n",
|
|
" Tight-binding hamiltonian H_tb.\n",
|
|
" \"\"\"\n",
|
|
" \n",
|
|
" # TODO: Kijk nog eens kritisch naar de omschrijving hierboven van de functie.\n",
|
|
" \n",
|
|
" # Luckily, the function is built in such a way it can also\n",
|
|
" # handle an array input as its first argument.\n",
|
|
" delta = atomic_basis(w, Ei, sigma)\n",
|
|
" \n",
|
|
" rho = np.sum(delta, axis=1)\n",
|
|
" \n",
|
|
" # Now normalize rho.\n",
|
|
" N = integrate(rho, w)\n",
|
|
" rho /= N\n",
|
|
" \n",
|
|
" return rho"
|
|
]
|
|
},
|
|
{
|
|
"attachments": {
|
|
"dosN010.png": {
|
|
"image/png": 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"
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},
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"dosN100.png": {
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"image/png": 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"
|
|
}
|
|
},
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "b2049bb4d5fb56c59e7d0e742a91d3c8",
|
|
"grade": false,
|
|
"grade_id": "cell-7560c4658b1da5d3",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 3.6 [3 points]\n",
|
|
"Use your density-of-states routine to calculate $\\rho(\\omega)$ for $n=10,20,40,80,100$ for $\\sigma_\\rho \\approx 0.005$. See below for two examples with $t \\approx -0.195$ and $n=10$ and $n=100$.\n",
|
|
"\n",
|
|
"Hint: if your plots look like they are smoothed out, try decreasing $\\sigma_\\rho$. If they look like there is a lot of noise, try increasing $\\sigma_\\rho$.\n",
|
|
"\n",
|
|
"$n = 10$ | $n = 100$\n",
|
|
":-: | :-:\n",
|
|
" | "
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 14,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "10cb847540f9e1998c9c1b40c5e43a7b",
|
|
"grade": true,
|
|
"grade_id": "cell-c3083a03553a2aa9",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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\n",
|
|
"text/plain": [
|
|
"<Figure size 1152x1152 with 6 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"sigma = .005\n",
|
|
"w = np.linspace(-.5, .5, 1000)\n",
|
|
"\n",
|
|
"fig, axs = plt.subplots(3, 2, sharex='col', figsize=(16,16))#, sharey='row'\n",
|
|
"\n",
|
|
"for i, n in enumerate([10, 20, 40, 80, 100]):\n",
|
|
" H_tb = TBHamiltonian(n)\n",
|
|
" # TODO: Decide whether to implement this + 1 - 1 trick here or in QREig above.\n",
|
|
" E_m = QREig(H_tb + np.eye(n)) - 1\n",
|
|
" DOS = getDOS_ED(w, E_m, sigma)\n",
|
|
" \n",
|
|
" ax = axs[i//2][i%2]\n",
|
|
" ax.plot(w, DOS, label=\"n = {}\".format(n))\n",
|
|
" ax.set_xlabel(\"$\\\\omega$\")\n",
|
|
" ax.set_ylabel(\"$\\\\rho(\\\\omega)$\")\n",
|
|
" ax.grid()\n",
|
|
" ax.set_title(\"n = {}\".format(n))\n",
|
|
" \n",
|
|
"\n",
|
|
"fig.suptitle(\"Density of states $\\\\rho(\\\\omega)$ for different chain lengths $n$\")\n",
|
|
"fig.tight_layout()\n",
|
|
"fig.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "69c457b9ef8fbd13ad935fe12c37c81c",
|
|
"grade": false,
|
|
"grade_id": "cell-362439917c95705f",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"## Step 4: Tight-Binding Propagation Method\n",
|
|
"\n",
|
|
"Now we turn to the time-dependent Schrödinger equation\n",
|
|
"\n",
|
|
"\\begin{align}\n",
|
|
" i\\hbar\\frac{\\partial}{\\partial t} \\psi(x,t) = H \\psi(x,t),\n",
|
|
"\\end{align}\n",
|
|
"\n",
|
|
"which has the formal solution\n",
|
|
"\n",
|
|
"\\begin{align}\n",
|
|
" \\psi(x,t) = U(t) \\psi(x,t=0),\n",
|
|
"\\end{align}\n",
|
|
"\n",
|
|
"with \n",
|
|
"\n",
|
|
"\\begin{align}\n",
|
|
" U(t) = e^{-i \\hbar H t}\n",
|
|
"\\end{align}\n",
|
|
"\n",
|
|
"being the time-propagation operator. Within the propagation method we can calculate the so-called local density-of-states\n",
|
|
"\n",
|
|
"\\begin{align}\n",
|
|
" \\rho_{loc}(\\omega) = \\frac{1}{2\\pi} \\int_{-\\infty}^{+\\infty} \\, e^{i\\omega t} \\, f(t) \\ dt,\n",
|
|
"\\end{align}\n",
|
|
"\n",
|
|
"with respect to an (arbitrary) initial state $\\psi(x,t=0)$, where\n",
|
|
"\n",
|
|
"\\begin{align}\n",
|
|
" f(t) &= \\int_{-\\infty}^{+\\infty} \\, \\psi^*(x,t) \\, \\psi(x,t=0) \\, dx \\\\\n",
|
|
" &\\approx \\int_{-\\infty}^{+\\infty} \\sum_i c_i^*(t) \\phi(x,x_i,\\sigma) \\, \\sum_j c_j(0) \\phi(x,x_j,\\sigma) \\, dx \\notag \\\\\n",
|
|
" &\\approx \\sum_i c_i^*(t) c_i(0). \\notag\n",
|
|
"\\end{align}\n",
|
|
"\n",
|
|
"Thus, the time propagation of an initial state towards positive *and* negative times followed by a Fourier transform of $f(t)$ yields the local density-of-states. To obtain the full density-of-states we need to average $\\rho_{loc}(\\omega)$ as follows\n",
|
|
"\n",
|
|
"\\begin{align}\n",
|
|
" \\rho(\\omega) = \\lim_{S \\to \\infty} \\frac{1}{S} \\sum_p^S \\rho^{(p)}_{loc}(\\omega)\n",
|
|
"\\end{align}\n",
|
|
"\n",
|
|
"over a variety of *random* initial states $p$.\n",
|
|
"\n",
|
|
"### Task 4.1 [3 points]\n",
|
|
"Implement a function which calculates the exact time-propagation matrix $U(\\tau)$ for a small time-step $\\tau$ given the Hamiltonian $H$. For simplicity, set $\\hbar = 1$ in the following. \n",
|
|
"\n",
|
|
"Hint: Use Scipy's $\\text{expm()}$ function."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "6cb01e4b3c6c192a0df3c4111b91c8fa",
|
|
"grade": true,
|
|
"grade_id": "cell-42a7aac3f0fa4d1b",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def getU_exact(tau, H):\n",
|
|
" # YOUR CODE HERE\n",
|
|
" raise NotImplementedError()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "79f8101b73fbb28ff9138437e9767178",
|
|
"grade": false,
|
|
"grade_id": "cell-9b02ad5515424242",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 4.2 [3 points]\n",
|
|
"Implement a function which performs the step-by-step time propagation given an initial state $\\vec{c}(0)$, the matrix $U(\\tau)$ and the discretized time grid $t_j$. In other words, your function should calculate \n",
|
|
"\n",
|
|
"$$\\vec{c}(j+1) = U(\\tau) \\cdot \\vec{c}(j)$$ \n",
|
|
"\n",
|
|
"for all $j$ of a given discretized time grid $t_j = j \\tau$."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "dc040cc32e832b097bfb8c367f4203a1",
|
|
"grade": true,
|
|
"grade_id": "cell-4e444f44bf3bc9c1",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def timePropagate(U, c0, t):\n",
|
|
" # YOUR CODE HERE\n",
|
|
" raise NotImplementedError()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "61362905e7a2d19219ae21f10a417823",
|
|
"grade": false,
|
|
"grade_id": "cell-62bfe608c358ff6d",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 4.3 [4 points]\n",
|
|
"Use both of the above functions to calculate and animate the time propagation of an initial state\n",
|
|
"\n",
|
|
"$$\\psi(x,t=0) = \\phi(x, x_{i=n/2}, \\sigma) \\leftrightarrow \\vec{c}(0) = [c_{i=n/2}(0) = 1, c_{i\\neq n/2}(0) = 0]$$\n",
|
|
"\n",
|
|
"for a $n=100$ chain. Discretize your time grid as $t_j=j\\tau$ with $j=0 \\dots 200$, and $\\tau=1.5$. Use again $a = 1$ and $\\sigma=0.25$. \n",
|
|
"\n",
|
|
"To plot / animate the time propagation you should plot the real-space wave function $\\psi(x,t) \\approx \\sum_i c_i(t) \\phi(x, x_i, \\sigma)$.\n",
|
|
"\n",
|
|
"Hint: use your function from task 3.4 to get the Hamiltonian $H$.\n",
|
|
"\n",
|
|
"For the animation you can use the following draft:\n",
|
|
"```python\n",
|
|
"# use matplotlib's animation package\n",
|
|
"import matplotlib.pylab as plt\n",
|
|
"import matplotlib\n",
|
|
"import matplotlib.animation as animation\n",
|
|
"# set the animation style to \"jshtml\" (for the use in Jupyter)\n",
|
|
"matplotlib.rcParams['animation.html'] = 'jshtml'\n",
|
|
"\n",
|
|
"# create a figure for the animation\n",
|
|
"fig = plt.figure()\n",
|
|
"plt.grid(True)\n",
|
|
"plt.xlim( ... ) # fix x limits\n",
|
|
"plt.ylim( ... ) # fix y limits\n",
|
|
"\n",
|
|
"# Create an empty plot object and prevent its showing (we will fill it each frame)\n",
|
|
"myPlot, = plt.plot([0], [0])\n",
|
|
"plt.close()\n",
|
|
"\n",
|
|
"# This function is called each frame to generate the animation (f is the frame number)\n",
|
|
"def animate(f): \n",
|
|
" myPlot.set_data( ... ) # update plot\n",
|
|
"\n",
|
|
"# Show the animation\n",
|
|
"frames = np.arange(1, np.size(t)) # t is the time grid here\n",
|
|
"myAnimation = animation.FuncAnimation(fig, animate, frames, interval = 20)\n",
|
|
"myAnimation\n",
|
|
"```"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "dac0e917be4cfe57c7d30715f3f61912",
|
|
"grade": true,
|
|
"grade_id": "cell-dd676b90f6a61df6",
|
|
"locked": false,
|
|
"points": 4,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# YOUR CODE HERE\n",
|
|
"raise NotImplementedError()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "6786036a70e4fffbda4c92e340ff90de",
|
|
"grade": true,
|
|
"grade_id": "cell-70e223783d806888",
|
|
"locked": false,
|
|
"points": 0,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Animate here ...\n",
|
|
"\n",
|
|
"# YOUR CODE HERE\n",
|
|
"raise NotImplementedError()\n",
|
|
"\n",
|
|
"# Yann has an animation about an atomic orbital that starts\n",
|
|
"# moving to left and right and then bounce back."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "74ab18f8b5e98bc5456ef221449f9299",
|
|
"grade": false,
|
|
"grade_id": "cell-0395602360fd9e4c",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 4.4 [3 points]\n",
|
|
"Implement a function which calculates the Crank-Nicolson time-propagation matrix \n",
|
|
"\n",
|
|
"\\begin{align*}\n",
|
|
" U_{CN}(\\tau) = (I - i \\tau H / 2)\\cdot(I + i \\tau H / 2)^{-1}.\n",
|
|
"\\end{align*}\n",
|
|
"\n",
|
|
"Here, $I$ is the diagonal identity matrix. Use Numpy's $\\text{inv()}$ function to invert the needed expression."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "1b2677753953d9a528f0dbb71d4077bb",
|
|
"grade": true,
|
|
"grade_id": "cell-d74914e5d0a13365",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def getU_CN(tau, H):\n",
|
|
" # YOUR CODE HERE\n",
|
|
" raise NotImplementedError()\n",
|
|
"\n",
|
|
"# Yann notes that the definition of $U_{CN}(\\tau)$ here is a little\n",
|
|
"# different from what Malte used on the slides. He recommends using\n",
|
|
"# what is stated here."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "3746f3298575d0e0c37d35c01039e60e",
|
|
"grade": false,
|
|
"grade_id": "cell-1daec83575502040",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 4.5 [5 points]\n",
|
|
"Implement a function which calculates the time-propagation matrix using the Trotter-Suzuki decomposition \n",
|
|
"\n",
|
|
"\\begin{align*}\n",
|
|
" U_{TZ}(\\tau) = e^{-i\\tau H_1} \\cdot e^{-i \\tau H_2}.\n",
|
|
"\\end{align*}\n",
|
|
"\n",
|
|
"In this approach you choose a decomposition of the tight-binding Hamiltonian $H = H_1 + H_2$, which allows you to analytically diagonalize $H_1$ and $H_2$ (see last lecture). From this analytic diagonalization you will be able to calculate the matrix exponentials $e^{-i\\tau H_1}$ and $e^{-i \\tau H_2}$.\n",
|
|
"\n",
|
|
"Write your definition of the 2x2 blocks in $e^{-i\\tau H_1}$ and $e^{-i \\tau H_2}$ in the Markdown cell below. (Double click on \"YOUR ANSWER HERE\" to open the cell, and ctrl+enter to compile.) "
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "566fe9a7f8031baea9812438b155671c",
|
|
"grade": true,
|
|
"grade_id": "cell-bef909a443eb2a68",
|
|
"locked": false,
|
|
"points": 2,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"YOUR ANSWER HERE"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "f9f25759b1a81bbac8c1834c2f4565b8",
|
|
"grade": true,
|
|
"grade_id": "cell-1425de6027596dea",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"def getU_TZ(tau, H):\n",
|
|
" # YOUR CODE HERE\n",
|
|
" raise NotImplementedError()\n",
|
|
"\n",
|
|
"# Yann mentions again that this is slightly different wrong what\n",
|
|
"# is in the slides/lecture."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "1747285f36e24921cb5c2811632f33c3",
|
|
"grade": false,
|
|
"grade_id": "cell-f53dc443bd1858b1",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 4.6 [3 points]\n",
|
|
"In your implementation of $U_{TZ}(\\tau)$ you analytically evaluate the matrix exponentials $e^{-i\\tau H_1}$ and $e^{-i \\tau H_2}$. Test your implementation by comparing your results for these matrix exponentials to those obtained using Scipy's $\\text{expm()}$ function."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "684e4173792cb10809386ef097c561e4",
|
|
"grade": true,
|
|
"grade_id": "cell-5aa3ffce9359fa7e",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# YOUR CODE HERE\n",
|
|
"raise NotImplementedError()\n",
|
|
"\n",
|
|
"# Yann printed\n",
|
|
"#Biggest differences of U1 with Scipy:\n",
|
|
"#Real: 1e-16 \n",
|
|
"#Imag: 2.77e-17\n",
|
|
"# \n",
|
|
"# and difference with U_exact in the order of 1e-1 or 1e-2."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "94ca5bdd479043f3c73214a3c4916923",
|
|
"grade": false,
|
|
"grade_id": "cell-c255a2bf5eac4e2b",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 4.7 [6 points]\n",
|
|
"In the next task you will need a Fourier transform to calculate the local density-of-states. Therefore you will need to implement a function that returns the Fourier transform $f(\\omega)$ of a given function $f(t)$ defined on a time grid $t$, for a given energy grid $\\omega$. I.e. it should calculate:\n",
|
|
"\n",
|
|
"\\begin{align}\n",
|
|
" f(\\omega) = \\frac{1}{2\\pi} \\int_{-\\infty}^{+\\infty} \\, e^{i\\omega t} \\, f(t) \\ dt.\n",
|
|
"\\end{align}\n",
|
|
"\n",
|
|
"Hint: use your integration function from task 2.2.\n",
|
|
"\n",
|
|
"Then implement a unit test for your function."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "37055009cb70e69bc9b1dbc761859c51",
|
|
"grade": true,
|
|
"grade_id": "cell-87ece8e50b1f8de5",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# YOUR CODE HERE\n",
|
|
"raise NotImplementedError()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "49aa23055a91a51494bcb9d64924cc75",
|
|
"grade": true,
|
|
"grade_id": "cell-46e1530333341bc6",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Implement your unit test here ...\n",
|
|
"\n",
|
|
"# YOUR CODE HERE\n",
|
|
"raise NotImplementedError()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "028bf13b6bf982c70fd1057c9d6f23f6",
|
|
"grade": false,
|
|
"grade_id": "cell-dc5656a6bdea875a",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 4.8 [3 points]\n",
|
|
"Calculate the local density-of-states $\\rho_{loc}(\\omega)$ from the Fourier transform of $f(t)$ using all three time propagation methods: $U(\\tau)$, $U_{CN}(\\tau)$ and $U_{TZ}(\\tau)$.\n",
|
|
"\n",
|
|
"Start from $\\psi(x,t=0) = \\phi(x, x_{i=0}, \\sigma)$ and $\\psi(x,t=0) = \\phi(x, x_{i=n/2}, \\sigma)$, using a $n=100$ chain. Discretize your integration time grid as $t_j=j\\tau$, with $j=-150 \\dots 150$ and $\\tau=1.5$. Use again $a = 1$ and $\\sigma=0.25$.\n",
|
|
"\n",
|
|
"Be careful: for the Fourier transform you will need positive *and* negative time steps! Thus you will need to do two time propagations: one using $U(\\tau)$ towards positive times and one using $U(-\\tau)$ towards negative times, both starting from $\\psi(x,t=0)$."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "29ff620823bca3839839fbc35ba9b236",
|
|
"grade": true,
|
|
"grade_id": "cell-316f9c26031f89df",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# YOUR CODE HERE\n",
|
|
"raise NotImplementedError()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "1c27de03eb5f84673d52e1e621c316ee",
|
|
"grade": true,
|
|
"grade_id": "cell-d7a678fdeef64ea2",
|
|
"locked": false,
|
|
"points": 0,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Do your own testing here ...\n",
|
|
"\n",
|
|
"# YOUR CODE HERE\n",
|
|
"raise NotImplementedError()\n",
|
|
"\n",
|
|
"# Yann had a plot for Tau = 1.5\n",
|
|
"# DOS: looking like a hill (\"like a dome with a peak around zero energy 0\")\n",
|
|
"# for CN, TS and the exact one\n",
|
|
"# a plot of f(t)\n",
|
|
"# a plot of local DOS\n",
|
|
"# in the title he mentiones the inital values."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"deletable": false,
|
|
"editable": false,
|
|
"nbgrader": {
|
|
"cell_type": "markdown",
|
|
"checksum": "c3e0ecb1b67f93590abf1a796bd507b8",
|
|
"grade": false,
|
|
"grade_id": "cell-ffbf1e8460ac69d8",
|
|
"locked": true,
|
|
"schema_version": 3,
|
|
"solution": false,
|
|
"task": false
|
|
}
|
|
},
|
|
"source": [
|
|
"### Task 4.9 [6 points]\n",
|
|
"Use the Trotter-Suzuki decomposition to calculate the full density-of-states by averaging over about $100$ local density-of-states you obtained from the time propagation of $100$ random initial states $\\vec{c}(0)$. To this end, you will need to make sure that each $\\vec{c}(0)$ is (a) normalized and (b) can have positive *and* negative elements. \n",
|
|
"\n",
|
|
"Compare this approximation to the total density-of-states to the exact one from task 3.6, which you obtained directly from the eigenvalues.\n",
|
|
"\n",
|
|
"Hint: don't expect the results to be the exact same. Check for the location of the peaks, and whether they have a similar order of magnitude.\n",
|
|
"\n",
|
|
"Hint: if you did not get the Trotter-Suzuki decomposition to work, you can instead use the exact or the Crank-Nicolson time-propagation matrix."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "81edbb8d07068d29021696fd87a961ba",
|
|
"grade": true,
|
|
"grade_id": "cell-2493a46a63277eda",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# YOUR CODE HERE\n",
|
|
"raise NotImplementedError()\n",
|
|
"\n",
|
|
"# Yann says the initial states do need to be negative, too."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"deletable": false,
|
|
"nbgrader": {
|
|
"cell_type": "code",
|
|
"checksum": "5438067dfec55e69ee224e67178d9e36",
|
|
"grade": true,
|
|
"grade_id": "cell-a40dfcd993da467c",
|
|
"locked": false,
|
|
"points": 3,
|
|
"schema_version": 3,
|
|
"solution": true,
|
|
"task": false
|
|
}
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Do your plotting here ...\n",
|
|
"\n",
|
|
"# YOUR CODE HERE\n",
|
|
"raise NotImplementedError()\n",
|
|
"\n",
|
|
"# Yann plotted the exact diagonalisation and the TS propagation results\n",
|
|
"# he had two plots, one peaky, one with peaks on the edges (looking a little\n",
|
|
"# like my 1f/2f results in my bachelor internship hmmpfff)"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Python 3",
|
|
"language": "python",
|
|
"name": "python3"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
|
"version": "3.8.10"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 4
|
|
}
|