{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import sisl\n", "from hubbard import HubbardHamiltonian, sp2, density, plot\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Isolated structures (molecules)\n", "\n", "In this example we study the effect of on-site Coulomb interactions for electrons in a carbon-based molecular geometry by solving the mean-field Hubbard equation\n", "\n", "We will start by building the geometry and the TB Hamiltonian for an sp2 carbon-based structure using `sisl`. The geometry will be read with `sisl` from this [file](https://github.com/dipc-cc/hubbard/blob/master/examples/molecules/clar-goblet/clar-goblet.xyz)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Build sisl.Geometry object\n", "geom = sisl.get_sile('../../examples/molecules/clar-goblet/clar-goblet.xyz').read_geometry()\n", "\n", "# Plot geometry: Carbon atoms in gray, Hydrogen atoms in white\n", "p = plot.GeometryPlot(geom, cmap='Greys')\n", "# This is just to plot Hydrogen atoms in white\n", "p.paux.set_clim(0, 0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To build the TB Hamiltonian (which describes the kinetic part of the system's Hamiltonian) one can use the function from the `hubbard` package `sp2` that builds the TB `sisl.Hamiltonian` of an sp2 carbon system. In this example we will use the first nearest neighbors interactions (1NN) TB model, typically used to simulate graphene-based nanostructures." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# Build sisl.Hamiltonian object using the sp2 function\n", "H0 = sp2(geom, t1=2.7, t2=0., t3=0., spin='polarized')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The second step is to build the `HubbardHamiltonian` object, which will enable the routines to iterate the mean field Hubbard Hamiltonian until it finds the self-consistent solution (convergence). To model the interaction part (Hubbard term) we will use `U=3.5` eV. See for instance [Nature Communications 10, 200 (2019)](https://www.nature.com/articles/s41467-018-08060-6) for reference." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# Build the HubbardHamiltonian object with U=3.5.\n", "# One can set the total number of up/down spin electrons by passing q=(q_up, q_dn). In this case, since there\n", "# is an even total number of electrons we can start with q=(ntot/2, ntot/2).\n", "HH = HubbardHamiltonian(H0, q=(len(H0)/2, len(H0)/2), U=3.5, kT=0.025)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Important note before starting the convergence process\n", "It is important to give an initial spin-density that breaks the symmetry between the up- and down- spin channels to start the convergence of the `HubbardHamiltonian` object. Otherwise the code *will not be able to find a solution*.\n", "Furthermore, the closer the initial spin-densities are to the self-consistent solution, the faster the code will find it." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "HH.set_polarization([2,6,10], dn=[24,28,32])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can start the convergence until we find the self-consistent solution up to a desired tolerance (`tol`) by calling the `HubbardHamiltonian.converge` method. This method needs as a mandatory argument another function that returns the spin-densities, since depending on the system or the boundary conditions the spin-densities will be obtain differently. For instance, to compute the spin-densities for TB Hamiltonians with *finite or periodic* boundary conditions, one can use the method `hubbard.density.calc_n`." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " HubbardHamiltonian: converge towards tol=1.00e-10\n", " 1 iterations completed: 0.5000000000000189 -179.259792397134\n", " 2 iterations completed: 0.06187870540897589 -246.48339932965422\n", " 3 iterations completed: 0.03262766358907587 -246.46128463327622\n", " 4 iterations completed: 0.005577074762743162 -246.54288102974022\n", " 5 iterations completed: 0.001590695329941716 -246.58392834159875\n", " 6 iterations completed: 0.0003939518266086184 -246.60028150400262\n", " 7 iterations completed: 3.853298342204603e-05 -246.59823272972324\n", " 8 iterations completed: 1.2569131205786288e-05 -246.5983134009241\n", " 9 iterations completed: 2.066709302139813e-06 -246.59817956357304\n", " 10 iterations completed: 7.121974041623957e-07 -246.5982066363112\n", " 11 iterations completed: 9.207019807666583e-08 -246.59819647159546\n", " 12 iterations completed: 3.800878933812868e-08 -246.59819631460275\n", " 13 iterations completed: 6.7612268006556064e-09 -246.5981962066005\n", " 14 iterations completed: 5.77773884291588e-10 -246.59819622793466\n", " 15 iterations completed: 1.38511535574537e-10 -246.59819622660737\n", " 16 iterations completed: 3.960010097614486e-11 -246.59819622643164\n", " found solution in 16 iterations\n" ] } ], "source": [ "# Converge until a tolerance of tol=1e-10\n", "dn = HH.converge(density.calc_n, tol=1e-10, print_info=True, steps=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Understanding the final results\n", "Now one can visualize some meaningful physical quantities and properties of the solution, e.g. such as the spin polarization. Other interesting electronic properties can be visualized using the `hubbard.plot` module.\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Let's visualize some relevant physical quantities of the final result (this process may take a few seconds)\n", "# By passing the argument ext_geom one can plot the spin polarization using the full geometry for the sp2 system\n", "# e.g. including Hydrogen atoms. Otherwise it only displays the pi-network structure\n", "p = plot.SpinPolarization(HH, colorbar=True, vmax=0.4, vmin=-0.4, ext_geom=geom)\n", "p.annotate()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Total energy = -246.59819622643164\n" ] } ], "source": [ "# Print total energy\n", "print(f\"Total energy = {HH.Etot}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Using output of the mean-field Hubbard model to start SIESTA calculation\n", "The `hubbard` package can be used to give a starting spin-density distribution for a more accurate spin polarized SIESTA calculation, by writing the spin densities to a `fdf-block`:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "# Write the self-consistent solution of the mean-field Hubbard calculation\n", "# to an input file for a SIESTA calculation.\n", "# ext_geom is the full sp2 geometry, e.g. that includes the Hydrogen atoms.\n", "# Otherwise it uses only the pi-network backbone structure stored in the H0 Hamiltonian\n", "HH.write_initspin('init-spin.fdf', ext_geom=geom)" ] } ], "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": "3.8.3" } }, "nbformat": 4, "nbformat_minor": 2 }