diff --git a/Examples/iptdmft_dlr.ipynb b/Examples/iptdmft_dlr.ipynb new file mode 100644 index 0000000..9a39c35 --- /dev/null +++ b/Examples/iptdmft_dlr.ipynb @@ -0,0 +1,307 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "329ad08d", + "metadata": {}, + "source": [ + "# Solution of the IPT-DMFT equations using the Discrete Lehman Representation\n", + "\n", + "This example is similar to Tutorial 1 in the ModelDMFT folder, but uses the discrete Lehmann representation (DLR) to represent the Green's functions and self-energies. Try repeating Tutorial 1 to converge the IPT equations for a given $\\beta$ and $U$. Check how much quicker your calculations are compared to Tutorial 1. Then obtain a Padé approximation of the spectral function $A(\\omega)$. For more information about the IPT equations, [(here)](https://doi.org/10.1103/PhysRevB.86.085133) is a good first reference, which this example follows closely." + ] + }, + { + "cell_type": "code", + "execution_count": 106, + "id": "ba3aecc3", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "\n", + "from triqs.gf import *\n", + "import numpy as np\n", + "from triqs.operators import *\n", + "\n", + "class IPTSolver:\n", + " def __init__(self, params):\n", + " self.params = params\n", + " # Matsubara frequency Green's functions\n", + " iw_mesh = MeshDLRImFreq(beta=params[\"beta\"], statistic='Fermion', w_max= params[\"w_max\"], eps =params[\"dlr_err\"], symmetrize = True)\n", + " self.G_iw = BlockGf(mesh=iw_mesh, gf_struct = [('up',1), ('dn',1)] )\n", + " self.G0_iw = self.G_iw.copy() # self.G0 will be set by the user after initialization\n", + " self.Sigma_iw = self.G_iw.copy()\n", + "\n", + " # Imaginary time\n", + " tau_mesh = MeshDLRImTime(beta=params[\"beta\"], statistic='Fermion', w_max= params[\"w_max\"], eps =params[\"dlr_err\"], symmetrize = True)\n", + " self.G0_tau = BlockGf(mesh=tau_mesh, gf_struct = [('up',1), ('dn',1)] )\n", + " self.G_tau = self.G0_tau.copy()\n", + " self.Sigma_tau = self.G0_tau.copy()\n", + "\n", + " def solve(self):\n", + " error = 1.0\n", + " iter = 0" + ] + }, + { + "cell_type": "code", + "execution_count": 112, + "id": "0287d987", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "params = {\n", + " \"beta\": 50.0,\n", + " \"mu\": 0.0,\n", + " \"alpha\" : 0.5,\n", + " \"w_max\": 10.0,\n", + " \"dlr_err\": 1e-8, \n", + " \"U\" : 3.0, # In the Mott state, U > 4, you run into trouble, but this is also why the IPT tutorial just stops at small iteration number. \n", + " \"t\" : 1.0,\n", + " \"max_iter\": 1000,\n", + " \"threshold\": 1e-8,\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 113, + "id": "bc6182a2", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Green Function G composed of 2 blocks: \n", + " Greens Function G_up with mesh DLR imfreq mesh of size 36 with beta = 50, statistic = Fermion, w_max = 10, eps = 1e-08 and target_shape (1, 1): \n", + " \n", + " Greens Function G_dn with mesh DLR imfreq mesh of size 36 with beta = 50, statistic = Fermion, w_max = 10, eps = 1e-08 and target_shape (1, 1): \n", + " " + ] + }, + "execution_count": 113, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "S = IPTSolver(params)\n", + "S.G_iw << SemiCircular(2*params[\"t\"])\n" + ] + }, + { + "cell_type": "code", + "execution_count": 114, + "id": "4d32a671", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Iteration: 1 Error: 0.4994691601105864\n", + "Iteration: 2 Error: 0.013218442183916101\n", + "Iteration: 3 Error: 0.006275825531574575\n", + "Iteration: 4 Error: 0.002993884912959155\n", + "Iteration: 5 Error: 0.0014307653808706133\n", + "Iteration: 6 Error: 0.0006841141729723721\n", + "Iteration: 7 Error: 0.00032711102854793284\n", + "Iteration: 8 Error: 0.0001563808101129327\n", + "Iteration: 9 Error: 7.474213040459254e-05\n", + "Iteration: 10 Error: 3.571384048717263e-05\n", + "Iteration: 11 Error: 1.719079397405343e-05\n", + "Iteration: 12 Error: 8.315824688021056e-06\n", + "Iteration: 13 Error: 4.021901271578088e-06\n", + "Iteration: 14 Error: 1.9448479028350008e-06\n", + "Iteration: 15 Error: 9.403252946849072e-07\n", + "Iteration: 16 Error: 4.545876733930143e-07\n", + "Iteration: 17 Error: 2.197414414872867e-07\n", + "Iteration: 18 Error: 1.0621059087778661e-07\n", + "Iteration: 19 Error: 5.1332351869159965e-08\n", + "Iteration: 20 Error: 2.4807740583998594e-08\n", + "Iteration: 21 Error: 1.1988382841998657e-08\n", + "Iteration: 22 Error: 5.7931588970383554e-09\n" + ] + } + ], + "source": [ + "error = 1.0\n", + "iter = 0\n", + "while error > params[\"threshold\"]:\n", + " for block, g in S.G0_iw:\n", + " g << inverse( iOmega_n - params[\"t\"]**2 * S.G_iw[block] )\n", + " S.G0_tau << make_gf_dlr_imtime(S.G0_iw)\n", + " S.Sigma_tau << (params[\"U\"]**2) * S.G0_tau * S.G0_tau * S.G0_tau\n", + " S.Sigma_iw << make_gf_dlr_imfreq(S.Sigma_tau)\n", + " G_old = S.G_iw.copy()\n", + " S.G_iw << inverse(inverse(S.G0_iw) - S.Sigma_iw)\n", + " S.G_iw << params[\"alpha\"]*S.G_iw+ (1-params[\"alpha\"])*G_old\n", + " G_tau_old = S.G_tau.copy()\n", + " S.G_tau << make_gf_dlr_imtime(S.G_iw)\n", + " error = np.max(np.abs((S.G_tau[\"up\"].data[:,0,0] - G_tau_old[\"up\"].data[:,0,0]))) # Compute absolute error\n", + " iter += 1\n", + "\n", + " print(\"Iteration:\", iter, \"Error:\", error)\n", + " if iter > params[\"max_iter\"]:\n", + " print(\"Maximum number of iterations reached without convergence\")\n", + " break" + ] + }, + { + "cell_type": "code", + "execution_count": 116, + "id": "50b5146d", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "G_tau_dense = make_gf_imtime(G_tau[\"up\"], n_tau=1000) # Obtain DLR expansion on dense imaginary time grid\n", + "\n", + "plt.figure(figsize = (10,10))\n", + "oplot(G_tau_dense.real, label = r\"$\\mathrm{Re}\\, G(\\tau)$ (DLR)\")\n", + "oplot(G_tau[\"up\"].real, marker = \"o\", markeredgecolor = \"black\", label = r\"$\\mathrm{Re}\\, G(\\tau)$ (DLR nodes)\")\n", + "plt.ylabel(\"\")\n", + "plt.legend(loc=\"upper right\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 121, + "id": "65fb461e", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "G_iw_dense = make_gf_imfreq(G_iw[\"up\"], n_iw = 5000) # Obtain DLR expansion on dense Matsubara frequency grid\n", + "\n", + "plt.figure(figsize = (10,10))\n", + "oplot(G_iw_dense.imag, marker = \"o\", markeredgecolor = \"red\", markersize=2, linestyle=\"none\", label = r\"Im $G(i \\omega_n)$ (DLR)\")\n", + "plt.xlim(-30,30)\n", + "plt.ylabel(\"\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 122, + "id": "e8703f85", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "Sigma_iw_dense = make_gf_imfreq(Sigma_iw[\"up\"], n_iw = 5000) # Obtain DLR expansion of self-energy on dense Matsubara frequency grid\n", + "\n", + "plt.figure(figsize = (10,10))\n", + "oplot(Sigma_iw_dense.imag, marker = \"o\", markeredgecolor = \"red\", markersize=2, linestyle=\"none\", label = r\"Im $\\Sigma(i \\omega_n)$ (DLR)\")\n", + "plt.xlim(-30,30)\n", + "plt.ylabel(\"\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 123, + "id": "1fa86573", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "G_w = Gf(mesh=MeshReFreq(window = (-5.0,5.0), n_w=1000), target_shape=[1,1])\n", + "G_iw = make_gf_imfreq(S.G_iw[\"up\"], n_iw = 2**14+3)\n", + "G_w.set_from_pade(G_iw, 100, 0.01) # Pade analytic continuation" + ] + }, + { + "cell_type": "code", + "execution_count": 124, + "id": "f18b5166", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize = (10,10))\n", + "oplot(-np.imag(G_w)/np.pi, marker = \"o\", markeredgecolor = \"black\", label = r\"$A(\\omega)$\")\n", + "plt.ylabel(\"\")\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "triqskernel", + "language": "python", + "name": "triqskernel" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/Examples/syk_dlr_cooling.ipynb b/Examples/syk_dlr_cooling.ipynb new file mode 100644 index 0000000..0a0ffca --- /dev/null +++ b/Examples/syk_dlr_cooling.ipynb @@ -0,0 +1,656 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "329ad08d", + "metadata": {}, + "source": [ + "# Self-consistent solution of the SYK equation using the Discrete Lehman Representation, with progressive cooling\n", + "\n", + "This example is similar to the tutorial \"Self-consistent solution of the SYK equation using the Discrete Lehmann Representation\", but it reaches low temperatures by using the calculation for a larger temperature as an initial guess for the next lowest temperature. While this does not appear to be necessary for the SYK model solves using fixed point iteration with mixing, it can be required in more complicated settings, and it is useful to see how the solution using a DLR grid for one temperature can be interpolated to a DLR grid for a lower temperature. " + ] + }, + { + "cell_type": "code", + "execution_count": 104, + "id": "1e11d3ed", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Iteration: 1 Error: 0.08341268718616414\n", + "Iteration: 2 Error: 0.020624876522001262\n", + "Iteration: 3 Error: 0.008508362270219227\n", + "Iteration: 4 Error: 0.004128924998232253\n", + "Iteration: 5 Error: 0.002140514522045611\n", + "Iteration: 6 Error: 0.0011588001998710795\n", + "Iteration: 7 Error: 0.000641626565325959\n", + "Iteration: 8 Error: 0.0003685756237916671\n", + "Iteration: 9 Error: 0.00021545130661632106\n", + "Iteration: 10 Error: 0.00012725475457886493\n", + "Iteration: 11 Error: 7.583129203281302e-05\n", + "Iteration: 12 Error: 4.614611609254915e-05\n", + "Iteration: 13 Error: 2.8492743066987902e-05\n", + "Iteration: 14 Error: 1.772916584391604e-05\n", + "Iteration: 15 Error: 1.1111730505386497e-05\n", + "Iteration: 16 Error: 7.011361329800625e-06\n", + "Iteration: 17 Error: 4.492548279610986e-06\n", + "Iteration: 18 Error: 2.9235559191875815e-06\n", + "Iteration: 19 Error: 1.9132391210208155e-06\n", + "Iteration: 20 Error: 1.2584982634900044e-06\n", + "Iteration: 21 Error: 8.316886299097881e-07\n", + "Iteration: 22 Error: 5.519602330195106e-07\n", + "Iteration: 23 Error: 3.67725420280518e-07\n", + "Iteration: 24 Error: 2.464355425280118e-07\n", + "Iteration: 25 Error: 1.672267073704603e-07\n", + "Iteration: 26 Error: 1.1382290110439897e-07\n", + "Iteration: 27 Error: 7.769105275778898e-08\n", + "Iteration: 28 Error: 5.3166422320227724e-08\n", + "Iteration: 29 Error: 3.6470967579305125e-08\n", + "Iteration: 30 Error: 2.5074259502044782e-08\n", + "Iteration: 31 Error: 1.7274895292018755e-08\n", + "Iteration: 32 Error: 1.1924811138541713e-08\n", + "Iteration: 33 Error: 8.25099566448273e-09\n", + "Iteration: 1 Error: 0.12500000000000008\n", + "Iteration: 2 Error: 0.09374268479504318\n", + "Iteration: 3 Error: 0.07029982706555926\n", + "Iteration: 4 Error: 0.05271881593527811\n", + "Iteration: 5 Error: 0.03953437914427471\n", + "Iteration: 6 Error: 0.0296472380023598\n", + "Iteration: 7 Error: 0.02223282692776435\n", + "Iteration: 8 Error: 0.016672733664746753\n", + "Iteration: 9 Error: 0.01250319084681556\n", + "Iteration: 10 Error: 0.00937641667570377\n", + "Iteration: 11 Error: 0.007031611962521944\n", + "Iteration: 12 Error: 0.005273206364277583\n", + "Iteration: 13 Error: 0.003954543887726147\n", + "Iteration: 14 Error: 0.002965648462529502\n", + "Iteration: 15 Error: 0.002224049531005301\n", + "Iteration: 16 Error: 0.0016679024097254747\n", + "Iteration: 17 Error: 0.0012508294622219363\n", + "Iteration: 18 Error: 0.0009380516473310729\n", + "Iteration: 19 Error: 0.0007034876659879896\n", + "Iteration: 20 Error: 0.0005275786694697304\n", + "Iteration: 21 Error: 0.0003956570385000857\n", + "Iteration: 22 Error: 0.00029672314351020246\n", + "Iteration: 23 Error: 0.0002225280395184437\n", + "Iteration: 24 Error: 0.00016688557566552076\n", + "Iteration: 25 Error: 0.00012515654005057497\n", + "Iteration: 26 Error: 9.38618129101565e-05\n", + "Iteration: 27 Error: 7.039226320310066e-05\n", + "Iteration: 28 Error: 5.2791193673074055e-05\n", + "Iteration: 29 Error: 3.959119081103912e-05\n", + "Iteration: 30 Error: 2.9691773912376984e-05\n", + "Iteration: 31 Error: 2.2267640184647775e-05\n", + "Iteration: 32 Error: 1.669985456442813e-05\n", + "Iteration: 33 Error: 1.2524246393363914e-05\n", + "Iteration: 34 Error: 9.392710038247376e-06\n", + "Iteration: 35 Error: 7.044182616988692e-06\n", + "Iteration: 36 Error: 5.282878921430978e-06\n", + "Iteration: 37 Error: 3.9619687982050955e-06\n", + "Iteration: 38 Error: 2.971336049595319e-06\n", + "Iteration: 39 Error: 2.228398234216389e-06\n", + "Iteration: 40 Error: 1.6712219777503812e-06\n", + "Iteration: 41 Error: 1.2533597891772885e-06\n", + "Iteration: 42 Error: 9.399779175578438e-07\n", + "Iteration: 43 Error: 7.049524244351346e-07\n", + "Iteration: 44 Error: 5.286913672408744e-07\n", + "Iteration: 45 Error: 3.9650153488279827e-07\n", + "Iteration: 46 Error: 2.9736356965681665e-07\n", + "Iteration: 47 Error: 2.23013357558699e-07\n", + "Iteration: 48 Error: 1.6725311263732223e-07\n", + "Iteration: 49 Error: 1.2543471639148152e-07\n", + "Iteration: 50 Error: 9.407224282886872e-08\n", + "Iteration: 51 Error: 7.05513684140513e-08\n", + "Iteration: 52 Error: 5.291143939656351e-08\n", + "Iteration: 53 Error: 3.9682030883447794e-08\n", + "Iteration: 54 Error: 2.976037438706669e-08\n", + "Iteration: 55 Error: 2.2319427639416745e-08\n", + "Iteration: 56 Error: 1.673893773590507e-08\n", + "Iteration: 57 Error: 1.2553733053088934e-08\n", + "Iteration: 58 Error: 9.414950485897577e-09\n", + "Iteration: 1 Error: 0.03865133722137276\n", + "Iteration: 2 Error: 0.018614955093191582\n", + "Iteration: 3 Error: 0.00849894319439648\n", + "Iteration: 4 Error: 0.004151449709067834\n", + "Iteration: 5 Error: 0.0022407882157367\n", + "Iteration: 6 Error: 0.001293947788542471\n", + "Iteration: 7 Error: 0.0007925613454448088\n", + "Iteration: 8 Error: 0.0004953228320831449\n", + "Iteration: 9 Error: 0.0003210956323461134\n", + "Iteration: 10 Error: 0.00021225572469640852\n", + "Iteration: 11 Error: 0.00014157350157173454\n", + "Iteration: 12 Error: 9.512449446208437e-05\n", + "Iteration: 13 Error: 6.455228776086619e-05\n", + "Iteration: 14 Error: 4.460059330685384e-05\n", + "Iteration: 15 Error: 3.094499174538523e-05\n", + "Iteration: 16 Error: 2.154868335307869e-05\n", + "Iteration: 17 Error: 1.5053500964035127e-05\n", + "Iteration: 18 Error: 1.0545842114351167e-05\n", + "Iteration: 19 Error: 7.406607351878591e-06\n", + "Iteration: 20 Error: 5.213626325606402e-06\n", + "Iteration: 21 Error: 3.677458260187283e-06\n", + "Iteration: 22 Error: 2.6163690330927025e-06\n", + "Iteration: 23 Error: 1.8739124811317787e-06\n", + "Iteration: 24 Error: 1.344099559652534e-06\n", + "Iteration: 25 Error: 9.653734328041175e-07\n", + "Iteration: 26 Error: 6.942194530901169e-07\n", + "Iteration: 27 Error: 4.998002283707059e-07\n", + "Iteration: 28 Error: 3.602129177160407e-07\n", + "Iteration: 29 Error: 2.598686162369468e-07\n", + "Iteration: 30 Error: 1.8765139586651713e-07\n", + "Iteration: 31 Error: 1.35621207431047e-07\n", + "Iteration: 32 Error: 9.809753021006173e-08\n", + "Iteration: 33 Error: 7.101042270862834e-08\n", + "Iteration: 34 Error: 5.1439938419939324e-08\n", + "Iteration: 35 Error: 3.728854830464812e-08\n", + "Iteration: 36 Error: 2.7047743489383436e-08\n", + "Iteration: 37 Error: 1.9631444303502832e-08\n", + "Iteration: 38 Error: 1.425690965284332e-08\n", + "Iteration: 39 Error: 1.0360738822434712e-08\n", + "Iteration: 40 Error: 7.575591098873957e-09\n", + "Iteration: 1 Error: 0.049500593527869674\n", + "Iteration: 2 Error: 0.025248973882357584\n", + "Iteration: 3 Error: 0.011473791465799965\n", + "Iteration: 4 Error: 0.005313178543824293\n", + "Iteration: 5 Error: 0.002757186074631879\n", + "Iteration: 6 Error: 0.001555958494719345\n", + "Iteration: 7 Error: 0.000924810665990039\n", + "Iteration: 8 Error: 0.000582492769565679\n", + "Iteration: 9 Error: 0.00037319900752930124\n", + "Iteration: 10 Error: 0.00024221618128450473\n", + "Iteration: 11 Error: 0.00016043382508984516\n", + "Iteration: 12 Error: 0.00010899462939217841\n", + "Iteration: 13 Error: 7.451134044311747e-05\n", + "Iteration: 14 Error: 5.120451625861833e-05\n", + "Iteration: 15 Error: 3.534504724711507e-05\n", + "Iteration: 16 Error: 2.4491624533329315e-05\n", + "Iteration: 17 Error: 1.702798477343226e-05\n", + "Iteration: 18 Error: 1.1873853163590908e-05\n", + "Iteration: 19 Error: 8.37383540475134e-06\n", + "Iteration: 20 Error: 5.944932320423035e-06\n", + "Iteration: 21 Error: 4.228969607944499e-06\n", + "Iteration: 22 Error: 3.0137481727421367e-06\n", + "Iteration: 23 Error: 2.1512691321667887e-06\n", + "Iteration: 24 Error: 1.5379336796295107e-06\n", + "Iteration: 25 Error: 1.100988416158355e-06\n", + "Iteration: 26 Error: 7.89193787875675e-07\n", + "Iteration: 27 Error: 5.66368540122486e-07\n", + "Iteration: 28 Error: 4.0690444713664675e-07\n", + "Iteration: 29 Error: 2.926380200385381e-07\n", + "Iteration: 30 Error: 2.1066118827128832e-07\n", + "Iteration: 31 Error: 1.517843921106099e-07\n", + "Iteration: 32 Error: 1.0945468209566656e-07\n", + "Iteration: 33 Error: 7.900879739342059e-08\n", + "Iteration: 34 Error: 5.749939974153406e-08\n", + "Iteration: 35 Error: 4.187316093862137e-08\n", + "Iteration: 36 Error: 3.051246461049928e-08\n", + "Iteration: 37 Error: 2.224711975751248e-08\n", + "Iteration: 38 Error: 1.6229762700437078e-08\n", + "Iteration: 39 Error: 1.1846234659884658e-08\n", + "Iteration: 40 Error: 8.651016625282892e-09\n", + "Iteration: 1 Error: 0.038585728716029\n", + "Iteration: 2 Error: 0.018631616234846382\n", + "Iteration: 3 Error: 0.008507043829109329\n", + "Iteration: 4 Error: 0.004159257050476817\n", + "Iteration: 5 Error: 0.002238088035525221\n", + "Iteration: 6 Error: 0.0012953692386866167\n", + "Iteration: 7 Error: 0.0007925729104717449\n", + "Iteration: 8 Error: 0.0004987279893976515\n", + "Iteration: 9 Error: 0.0003227268075990941\n", + "Iteration: 10 Error: 0.00021131286201181432\n", + "Iteration: 11 Error: 0.00013959161172744095\n", + "Iteration: 12 Error: 9.326699329281762e-05\n", + "Iteration: 13 Error: 6.42304424464113e-05\n", + "Iteration: 14 Error: 4.445856771168044e-05\n", + "Iteration: 15 Error: 3.089456088278819e-05\n", + "Iteration: 16 Error: 2.155061938646785e-05\n", + "Iteration: 17 Error: 1.507789453308872e-05\n", + "Iteration: 18 Error: 1.0580522994463326e-05\n", + "Iteration: 19 Error: 7.442226792275797e-06\n", + "Iteration: 20 Error: 5.24719866862311e-06\n", + "Iteration: 21 Error: 3.706706921069447e-06\n", + "Iteration: 22 Error: 2.6235552509357163e-06\n", + "Iteration: 23 Error: 1.8598860398455486e-06\n", + "Iteration: 24 Error: 1.3275314990623954e-06\n", + "Iteration: 25 Error: 9.55351666775961e-07\n", + "Iteration: 26 Error: 6.883872155083459e-07\n", + "Iteration: 27 Error: 4.965583417781971e-07\n", + "Iteration: 28 Error: 3.5857492264312896e-07\n", + "Iteration: 29 Error: 2.591776576132965e-07\n", + "Iteration: 30 Error: 1.8750993530103344e-07\n", + "Iteration: 31 Error: 1.3577200841385917e-07\n", + "Iteration: 32 Error: 9.839072123707382e-08\n", + "Iteration: 33 Error: 7.135376894895629e-08\n", + "Iteration: 34 Error: 5.178400364069802e-08\n", + "Iteration: 35 Error: 3.7606193048489445e-08\n", + "Iteration: 36 Error: 2.732776288594252e-08\n", + "Iteration: 37 Error: 1.9870334433402803e-08\n", + "Iteration: 38 Error: 1.4456322250389064e-08\n", + "Iteration: 39 Error: 1.0523064530865156e-08\n", + "Iteration: 40 Error: 7.663963463855339e-09\n" + ] + } + ], + "source": [ + "from triqs.gf import *\n", + "from triqs.gf.tools import *\n", + "from triqs.operators import *\n", + "from triqs.gf.block_gf import *\n", + "from triqs.gf.descriptors import Function\n", + "import h5\n", + "import numpy as np\n", + "from triqs.plot.mpl_interface import *\n", + "import matplotlib.pyplot as plt\n", + "import matplotlib as mpl\n", + "import json, sys, os\n", + "\n", + "params = {\n", + " \"beta\": 500.0,\n", + " \"mu\": 0.0,\n", + " \"alpha\" : 0.75,\n", + " \"w_max\": 10.0,\n", + " \"dlr_err\": 1e-12, \n", + " \"J\" : 1.0,\n", + " \"max_iter\": 1000,\n", + " \"threshold\": 1e-8,\n", + "}\n", + "\n", + "gf_struct =[('up',1), ('dn',1)]\n", + "iw_mesh = MeshDLRImFreq(beta=params[\"beta\"], statistic='Fermion', w_max= params[\"w_max\"], eps = params[\"dlr_err\"], symmetrize = True)\n", + "G_iw = BlockGf(mesh=iw_mesh, gf_struct=gf_struct)\n", + "G_tau = make_gf_dlr_imtime(G_iw)\n", + "Sigma_iw = G_iw.copy()\n", + "Sigma_tau = make_gf_dlr_imtime(Sigma_iw)\n", + "betas = np.array([50.0, 100.0, 200.0, 500.0, 1000.0]) # Different beta values for testing\n", + "\n", + "for i, beta in enumerate(betas):\n", + " gf_struct =[('up',1), ('dn',1)]\n", + " params[\"beta\"] = beta\n", + " \n", + " iw_mesh = MeshDLRImFreq(beta=params[\"beta\"], statistic='Fermion', w_max= params[\"w_max\"], eps = params[\"dlr_err\"], symmetrize = True)\n", + "\n", + " G_iw = BlockGf(mesh=iw_mesh, gf_struct=gf_struct)\n", + " G_tau = make_gf_dlr_imtime(G_iw)\n", + " Sigma_iw = G_iw.copy()\n", + " Sigma_tau = make_gf_dlr_imtime(Sigma_iw)\n", + " if i == 0:\n", + " G_iw << SemiCircular(1.0)\n", + " if i > 1:\n", + " tau = np.array([x.real for x in G_tau.mesh.values()], dtype=np.float64)\n", + " old_tau = np.array([x.real for x in G_old.mesh.values()], dtype=np.float64)\n", + " old_beta = np.max(old_tau)\n", + " tau_prime = tau*old_beta/params[\"beta\"]\n", + " G_dlr = make_gf_dlr(G_old)\n", + " for block, g in G_tau:\n", + " g.data[:,0,0] = np.array([G_dlr[\"up\"](t)[0,0] for t in tau_prime])\n", + " G_iw << make_gf_dlr_imfreq(G_tau)\n", + "\n", + " G_tau << make_gf_dlr_imtime(G_iw) # Initial guess in the imaginary time domain\n", + " error = 1.0\n", + " iter = 0\n", + "\n", + " while error > params[\"threshold\"]:\n", + " tau = np.array([x.real for x in G_tau.mesh.values()], dtype=np.float64) \n", + " for block, g in G_tau:\n", + " G_dlr = make_gf_dlr(g)\n", + " Sigma_tau[block].data[:,0,0] = np.array([G_dlr(t)[0,0]**2*G_dlr(params[\"beta\"]-t)[0,0] for t in tau]) # Compute self-energy in imaginary time\n", + "\n", + " Sigma_iw << make_gf_dlr_imfreq(Sigma_tau) # Transform self-energy to Matsubara frequency domain \n", + "\n", + " for block, g in G_tau:\n", + " G_iw[block] << inverse(iOmega_n - Sigma_iw[block]) # Solve the Dyson equation to obtain Green's function\n", + " G_old = G_tau.copy()\n", + " G_tau << params[\"alpha\"]*G_old + (1-params[\"alpha\"])*make_gf_dlr_imtime(G_iw) # Update Green's function via weighted fixed point iteration\n", + " error = np.max(np.abs((G_tau[\"up\"].data[:,0,0] - G_old[\"up\"].data[:,0,0]))) # Compute absolute error\n", + " iter += 1\n", + "\n", + " print(\"Iteration:\", iter, \"Error:\", error)\n", + " if iter > params[\"max_iter\"]:\n", + " print(\"Maximum number of iterations reached without convergence\")\n", + " break" + ] + }, + { + "cell_type": "code", + "execution_count": 105, + "id": "5e260dfb", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "G_tau_dense = make_gf_imtime(G_tau[\"up\"], n_tau=1000) # Obtain DLR expansion on dense imaginary time grid\n", + "t = np.array([x.real for x in G_tau_dense.mesh.values()])[1:] # Obtain dense grid\n", + "Gconformal = -np.pi**(1/4) / np.sqrt(2*params[\"beta\"]) * 1/np.sqrt(np.sin(np.pi * t / params[\"beta\"])) # Conformal solution\n", + "\n", + "plt.figure(figsize = (10,10))\n", + "oplot(G_tau_dense.real, label = r\"$\\mathrm{Re}\\, G(\\tau)$ (DLR)\")\n", + "oplot(G_tau[\"up\"].real, marker = \"o\", markeredgecolor = \"black\", label = r\"$\\mathrm{Re}\\, G(\\tau)$ (DLR nodes)\")\n", + "plt.plot(t, Gconformal, label = r\"$G_c(\\tau)$\", color = \"red\", linestyle = \"dashed\")\n", + "plt.ylim(-0.5,0)\n", + "plt.ylabel(\"\")\n", + "plt.legend(loc=\"upper left\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "45fedad2", + "metadata": {}, + "source": [ + "### Exercise 2 \n", + "\n", + "Next try repeating Tutorial 1 to converge the IPT equations for a given $\\beta$ and $U$. Check how much quicker your calculations are compared to Tutorial 1. Then obtain a Padé approximation of the spectral function $A(\\omega)$.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 106, + "id": "ba3aecc3", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "\n", + "from triqs.gf import *\n", + "import numpy as np\n", + "from triqs.operators import *\n", + "\n", + "class IPTSolver:\n", + " def __init__(self, params):\n", + " self.params = params\n", + " # Matsubara frequency Green's functions\n", + " iw_mesh = MeshDLRImFreq(beta=params[\"beta\"], statistic='Fermion', w_max= params[\"w_max\"], eps =params[\"dlr_err\"], symmetrize = True)\n", + " self.G_iw = BlockGf(mesh=iw_mesh, gf_struct = [('up',1), ('dn',1)] )\n", + " self.G0_iw = self.G_iw.copy() # self.G0 will be set by the user after initialization\n", + " self.Sigma_iw = self.G_iw.copy()\n", + "\n", + " # Imaginary time\n", + " tau_mesh = MeshDLRImTime(beta=params[\"beta\"], statistic='Fermion', w_max= params[\"w_max\"], eps =params[\"dlr_err\"], symmetrize = True)\n", + " self.G0_tau = BlockGf(mesh=tau_mesh, gf_struct = [('up',1), ('dn',1)] )\n", + " self.G_tau = self.G0_tau.copy()\n", + " self.Sigma_tau = self.G0_tau.copy()\n", + "\n", + " def solve(self):\n", + " error = 1.0\n", + " iter = 0" + ] + }, + { + "cell_type": "code", + "execution_count": 112, + "id": "0287d987", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "params = {\n", + " \"beta\": 50.0,\n", + " \"mu\": 0.0,\n", + " \"alpha\" : 0.5,\n", + " \"w_max\": 10.0,\n", + " \"dlr_err\": 1e-8, \n", + " \"U\" : 3.0, # In the Mott state, U > 4, you run into trouble, but this is also why the IPT tutorial just stops at small iteration number. \n", + " \"t\" : 1.0,\n", + " \"max_iter\": 1000,\n", + " \"threshold\": 1e-8,\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 113, + "id": "bc6182a2", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Green Function G composed of 2 blocks: \n", + " Greens Function G_up with mesh DLR imfreq mesh of size 36 with beta = 50, statistic = Fermion, w_max = 10, eps = 1e-08 and target_shape (1, 1): \n", + " \n", + " Greens Function G_dn with mesh DLR imfreq mesh of size 36 with beta = 50, statistic = Fermion, w_max = 10, eps = 1e-08 and target_shape (1, 1): \n", + " " + ] + }, + "execution_count": 113, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "S = IPTSolver(params)\n", + "S.G_iw << SemiCircular(2*params[\"t\"])\n" + ] + }, + { + "cell_type": "code", + "execution_count": 114, + "id": "4d32a671", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Iteration: 1 Error: 0.4994691601105864\n", + "Iteration: 2 Error: 0.013218442183916101\n", + "Iteration: 3 Error: 0.006275825531574575\n", + "Iteration: 4 Error: 0.002993884912959155\n", + "Iteration: 5 Error: 0.0014307653808706133\n", + "Iteration: 6 Error: 0.0006841141729723721\n", + "Iteration: 7 Error: 0.00032711102854793284\n", + "Iteration: 8 Error: 0.0001563808101129327\n", + "Iteration: 9 Error: 7.474213040459254e-05\n", + "Iteration: 10 Error: 3.571384048717263e-05\n", + "Iteration: 11 Error: 1.719079397405343e-05\n", + "Iteration: 12 Error: 8.315824688021056e-06\n", + "Iteration: 13 Error: 4.021901271578088e-06\n", + "Iteration: 14 Error: 1.9448479028350008e-06\n", + "Iteration: 15 Error: 9.403252946849072e-07\n", + "Iteration: 16 Error: 4.545876733930143e-07\n", + "Iteration: 17 Error: 2.197414414872867e-07\n", + "Iteration: 18 Error: 1.0621059087778661e-07\n", + "Iteration: 19 Error: 5.1332351869159965e-08\n", + "Iteration: 20 Error: 2.4807740583998594e-08\n", + "Iteration: 21 Error: 1.1988382841998657e-08\n", + "Iteration: 22 Error: 5.7931588970383554e-09\n" + ] + } + ], + "source": [ + "error = 1.0\n", + "iter = 0\n", + "while error > params[\"threshold\"]:\n", + " for block, g in S.G0_iw:\n", + " g << inverse( iOmega_n - params[\"t\"]**2 * S.G_iw[block] )\n", + " S.G0_tau << make_gf_dlr_imtime(S.G0_iw)\n", + " S.Sigma_tau << (params[\"U\"]**2) * S.G0_tau * S.G0_tau * S.G0_tau\n", + " S.Sigma_iw << make_gf_dlr_imfreq(S.Sigma_tau)\n", + " G_old = S.G_iw.copy()\n", + " S.G_iw << inverse(inverse(S.G0_iw) - S.Sigma_iw)\n", + " S.G_iw << params[\"alpha\"]*S.G_iw+ (1-params[\"alpha\"])*G_old\n", + " G_tau_old = S.G_tau.copy()\n", + " S.G_tau << make_gf_dlr_imtime(S.G_iw)\n", + " error = np.max(np.abs((S.G_tau[\"up\"].data[:,0,0] - G_tau_old[\"up\"].data[:,0,0]))) # Compute absolute error\n", + " iter += 1\n", + "\n", + " print(\"Iteration:\", iter, \"Error:\", error)\n", + " if iter > params[\"max_iter\"]:\n", + " print(\"Maximum number of iterations reached without convergence\")\n", + " break" + ] + }, + { + "cell_type": "code", + "execution_count": 116, + "id": "50b5146d", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "G_tau_dense = make_gf_imtime(G_tau[\"up\"], n_tau=1000) # Obtain DLR expansion on dense imaginary time grid\n", + "\n", + "plt.figure(figsize = (10,10))\n", + "oplot(G_tau_dense.real, label = r\"$\\mathrm{Re}\\, G(\\tau)$ (DLR)\")\n", + "oplot(G_tau[\"up\"].real, marker = \"o\", markeredgecolor = \"black\", label = r\"$\\mathrm{Re}\\, G(\\tau)$ (DLR nodes)\")\n", + "plt.ylabel(\"\")\n", + "plt.legend(loc=\"upper right\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 121, + "id": "65fb461e", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "G_iw_dense = make_gf_imfreq(G_iw[\"up\"], n_iw = 5000) # Obtain DLR expansion on dense Matsubara frequency grid\n", + "\n", + "plt.figure(figsize = (10,10))\n", + "oplot(G_iw_dense.imag, marker = \"o\", markeredgecolor = \"red\", markersize=2, linestyle=\"none\", label = r\"Im $G(i \\omega_n)$ (DLR)\")\n", + "plt.xlim(-30,30)\n", + "plt.ylabel(\"\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 122, + "id": "e8703f85", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "Sigma_iw_dense = make_gf_imfreq(Sigma_iw[\"up\"], n_iw = 5000) # Obtain DLR expansion of self-energy on dense Matsubara frequency grid\n", + "\n", + "plt.figure(figsize = (10,10))\n", + "oplot(Sigma_iw_dense.imag, marker = \"o\", markeredgecolor = \"red\", markersize=2, linestyle=\"none\", label = r\"Im $\\Sigma(i \\omega_n)$ (DLR)\")\n", + "plt.xlim(-30,30)\n", + "plt.ylabel(\"\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 123, + "id": "1fa86573", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "G_w = Gf(mesh=MeshReFreq(window = (-5.0,5.0), n_w=1000), target_shape=[1,1])\n", + "G_iw = make_gf_imfreq(S.G_iw[\"up\"], n_iw = 2**14+3)\n", + "G_w.set_from_pade(G_iw, 100, 0.01) # Pade analytic continuation" + ] + }, + { + "cell_type": "code", + "execution_count": 124, + "id": "f18b5166", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize = (10,10))\n", + "oplot(-np.imag(G_w)/np.pi, marker = \"o\", markeredgecolor = \"black\", label = r\"$A(\\omega)$\")\n", + "plt.ylabel(\"\")\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "triqskernel", + "language": "python", + "name": "triqskernel" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/ModelDMFT/06-SYK_DLR.ipynb b/ModelDMFT/06-SYK_DLR.ipynb new file mode 100644 index 0000000..bb9a8fe --- /dev/null +++ b/ModelDMFT/06-SYK_DLR.ipynb @@ -0,0 +1,66 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "329ad08d", + "metadata": {}, + "source": [ + "# Self-consistent solution of the SYK equation using the Discrete Lehmann Representation\n", + "\n", + "The goal of this tutorial is to showcase the use of the discrete Lehmann representation (DLR) to solve the Dyson equation self-consistently (i.e., given an expression for the self-energy in terms of the Green's function), by implementing a simple self-consistent loop for the Sachdev-Ye-Kitaev (SYK) model. For background on the DLR and its use in TRIQS, we refer to the [TRIQS documentation](https://triqs.github.io/triqs/latest/userguide/python/tutorials/Basics/solutions/01s-Greens_functions.html#Compact-meshes-for-imaginary-time-/-frequency:-DLR-Green%E2%80%99s-function). We note that although this is not a DMFT calculation, some of the main steps (Fourier transform between imaginary time and Matsubara frequency, solving the Dyson equation) are similar to those in a DMFT calculation." + ] + }, + { + "cell_type": "markdown", + "id": "fee0f10b", + "metadata": {}, + "source": [ + "### Constructing DLR Green's Functions\n", + "\n", + "We begin by setting various parameters, building a DLR imaginary frequency mesh, and creating Green's function and self-energy containers from this mesh. The DLR parameters are the desired accuracy, `dlr_error`, and the problem bandwidth or frequency cutoff, `w_max`. We also set some physical problem parameters, as well as a maximum number of iterations for the self-consistency, a self-consistency convergence tolerance, and a mixing parameter $\\alpha$." + ] + }, + { + "cell_type": "markdown", + "id": "d5547d81", + "metadata": {}, + "source": [ + "### Exercise 1 \n", + "We first solve the $0+1$-dimensional (impurity) Sachdev-Ye-Kitaev (SYK) model self-consistently. The Hamiltonian is given by \n", + "$$H = \\frac{1}{(2N)^{3/2}}\\sum^N_{ijkl} J_{ijkl} c^\\dagger_i c^\\dagger_j c_k c_l$$\n", + "where the $J_{ijkl}$ are random Gaussian couplings between $N$ fermions with constant variance $J^2$.\n", + " This model has many interesting applications for non-Fermi liquids, or strange metals, and quantum criticality. You can read more about the model and its extensions [(here)](https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.94.035004). Here we are interested in a simple form of the self-energy in the large-$N$ limit of the model, given by\n", + "\\begin{equation}\n", + "\\Sigma(\\tau) = -J^2 G^2(\\tau)G(-\\tau).\n", + "\\end{equation}\n", + "Combining this self-energy with the Dyson equation yields a self-consistent set of equations. These were solved using the DLR with weighted fixed point iteration in Sec. VII of [(this paper)](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.105.235115). Following that reference, it is your turn to write a self-consistent loop to solve for $G$.\n", + "\n", + "As shown in the paper, as we approach the $\\beta = \\infty$ limit, the result should begin to match the conformal solution of these equations. Try comparing to the conformal solution! We should already have quite good agreement at $\\beta = 1000$.\n", + "\\begin{equation}\n", + "G_c(\\tau)=-\\frac{\\pi^{1 / 4}}{\\sqrt{2 \\beta}}\\left(\\sin \\left(\\frac{\\pi \\tau}{\\beta}\\right)\\right)^{-1 / 2}\n", + "\\end{equation}" + ] + } + ], + "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": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/ModelDMFT/solutions/06s-SYK_DLR.ipynb b/ModelDMFT/solutions/06s-SYK_DLR.ipynb new file mode 100644 index 0000000..c7cacc3 --- /dev/null +++ b/ModelDMFT/solutions/06s-SYK_DLR.ipynb @@ -0,0 +1,253 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "329ad08d", + "metadata": {}, + "source": [ + "# Self-consistent solution of the SYK equation using the Discrete Lehmann Representation\n", + "\n", + "The goal of this tutorial is to showcase the use of the discrete Lehmann representation (DLR) to solve the Dyson equation self-consistently (i.e., given an expression for the self-energy in terms of the Green's function), by implementing a simple self-consistent loop for the Sachdev-Ye-Kitaev (SYK) model. For background on the DLR and its use in TRIQS, we refer to the [TRIQS documentation](https://triqs.github.io/triqs/latest/userguide/python/tutorials/Basics/solutions/01s-Greens_functions.html#Compact-meshes-for-imaginary-time-/-frequency:-DLR-Green%E2%80%99s-function). We note that although this is not a DMFT calculation, some of the main steps (Fourier transform between imaginary time and Matsubara frequency, solving the Dyson equation) are similar to those in a DMFT calculation." + ] + }, + { + "cell_type": "markdown", + "id": "fee0f10b", + "metadata": {}, + "source": [ + "### Constructing DLR Green's Functions\n", + "\n", + "We begin by setting various parameters, building a DLR imaginary frequency mesh, and creating Green's function and self-energy containers from this mesh. The DLR parameters are the desired accuracy, `dlr_error`, and the problem bandwidth or frequency cutoff, `w_max`. We also set some physical problem parameters, as well as a maximum number of iterations for the self-consistency, a self-consistency convergence tolerance, and a mixing parameter $\\alpha$." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "f916c67b", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "from triqs.gf import *\n", + "from triqs.gf.tools import *\n", + "from triqs.operators import *\n", + "from triqs.gf.block_gf import *\n", + "from triqs.gf.descriptors import Function\n", + "import h5\n", + "import numpy as np\n", + "from triqs.plot.mpl_interface import *\n", + "import matplotlib.pyplot as plt\n", + "import matplotlib as mpl\n", + "import json, sys, os\n", + "\n", + "params = {\n", + " \"beta\": 1000.0,\n", + " \"mu\": 0.0,\n", + " \"alpha\" : 0.75,\n", + " \"w_max\": 5.0,\n", + " \"dlr_err\": 1e-8, \n", + " \"J\" : 1.0,\n", + " \"max_iter\": 1000,\n", + " \"threshold\": 1e-8,\n", + "}\n", + "\n", + "gf_struct =[('up',1), ('dn',1)]\n", + "iw_mesh = MeshDLRImFreq(beta=params[\"beta\"], statistic='Fermion', w_max= params[\"w_max\"], eps = params[\"dlr_err\"], symmetrize = True)\n", + "G_iw = BlockGf(mesh=iw_mesh, gf_struct=gf_struct)\n", + "G_tau = make_gf_dlr_imtime(G_iw)\n", + "Sigma_iw = G_iw.copy()\n", + "Sigma_tau = make_gf_dlr_imtime(Sigma_iw)" + ] + }, + { + "cell_type": "markdown", + "id": "d5547d81", + "metadata": {}, + "source": [ + "### Exercise 1 \n", + "We first solve the $0+1$-dimensional (impurity) Sachdev-Ye-Kitaev (SYK) model self-consistently. The Hamiltonian is given by \n", + "$$H = \\frac{1}{(2N)^{3/2}}\\sum^N_{ijkl} J_{ijkl} c^\\dagger_i c^\\dagger_j c_k c_l$$\n", + "where the $J_{ijkl}$ are random Gaussian couplings between $N$ fermions with constant variance $J^2$.\n", + " This model has many interesting applications for non-Fermi liquids, or strange metals, and quantum criticality. You can read more about the model and its extensions [(here)](https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.94.035004). Here we are interested in a simple form of the self-energy in the large-$N$ limit of the model, given by\n", + "\\begin{equation}\n", + "\\Sigma(\\tau) = -J^2 G^2(\\tau)G(-\\tau).\n", + "\\end{equation}\n", + "Combining this self-energy with the Dyson equation yields a self-consistent set of equations. These were solved using the DLR with weighted fixed point iteration in Sec. VII of [(this paper)](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.105.235115). Following that reference, it is your turn to write a self-consistent loop to solve for $G$.\n", + "\n", + "As shown in the paper, as we approach the $\\beta = \\infty$ limit, the result should begin to match the conformal solution of these equations. Try comparing to the conformal solution! We should already have quite good agreement at $\\beta = 1000$.\n", + "\\begin{equation}\n", + "G_c(\\tau)=-\\frac{\\pi^{1 / 4}}{\\sqrt{2 \\beta}}\\left(\\sin \\left(\\frac{\\pi \\tau}{\\beta}\\right)\\right)^{-1 / 2}\n", + "\\end{equation}" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "5711f528", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Iteration: 1 Error: 0.09365042856328878\n", + "Iteration: 2 Error: 0.02389091857123847\n", + "Iteration: 3 Error: 0.017721420560846274\n", + "Iteration: 4 Error: 0.01225291280723799\n", + "Iteration: 5 Error: 0.0069780870343561854\n", + "Iteration: 6 Error: 0.003097888019241102\n", + "Iteration: 7 Error: 0.0011871083057315088\n", + "Iteration: 8 Error: 0.00045291431501309765\n", + "Iteration: 9 Error: 0.00020867659064766064\n", + "Iteration: 10 Error: 0.0001221937305567189\n", + "Iteration: 11 Error: 7.29518263504203e-05\n", + "Iteration: 12 Error: 4.423836621747501e-05\n", + "Iteration: 13 Error: 2.7150527487307397e-05\n", + "Iteration: 14 Error: 1.681698909905549e-05\n", + "Iteration: 15 Error: 1.0655920737845381e-05\n", + "Iteration: 16 Error: 6.883502771559691e-06\n", + "Iteration: 17 Error: 4.471739081024495e-06\n", + "Iteration: 18 Error: 2.9197014490001116e-06\n", + "Iteration: 19 Error: 1.9151486686519448e-06\n", + "Iteration: 20 Error: 1.2615741423749327e-06\n", + "Iteration: 21 Error: 8.343275527122884e-07\n", + "Iteration: 22 Error: 5.538040310781867e-07\n", + "Iteration: 23 Error: 3.6886194437757425e-07\n", + "Iteration: 24 Error: 2.4646771973335646e-07\n", + "Iteration: 25 Error: 1.6517766920909338e-07\n", + "Iteration: 26 Error: 1.1100690316956374e-07\n", + "Iteration: 27 Error: 7.485517372618489e-08\n", + "Iteration: 28 Error: 5.154431514942104e-08\n", + "Iteration: 29 Error: 3.558213140797406e-08\n", + "Iteration: 30 Error: 2.462116999168984e-08\n", + "Iteration: 31 Error: 1.7074547720152822e-08\n", + "Iteration: 32 Error: 1.1865782800768443e-08\n", + "Iteration: 33 Error: 8.262231621092297e-09\n" + ] + } + ], + "source": [ + "G_iw << SemiCircular(1.0) # Initial guess for the Green's function \n", + "G_tau << make_gf_dlr_imtime(G_iw) # Initial guess in the imaginary time domain\n", + "error = 1.0\n", + "iter = 0\n", + "\n", + "while error > params[\"threshold\"]:\n", + " for block, g in G_tau:\n", + " Sigma_tau[block].data[:,0,0] = params[\"J\"]**2 * g.data[:,0,0]**2*np.flip(g.data[:,0,0]) # Compute self-energy in imaginary time\n", + "\n", + " Sigma_iw << make_gf_dlr_imfreq(Sigma_tau) # Transform self-energy to Matsubara frequency domain \n", + "\n", + " for block, g in G_tau:\n", + " G_iw[block] << inverse(iOmega_n - Sigma_iw[block]) # Solve the Dyson equation to obtain Green's function\n", + " G_old = G_tau.copy()\n", + " G_tau << params[\"alpha\"]*G_old + (1-params[\"alpha\"])*make_gf_dlr_imtime(G_iw) # Update Green's function via weighted fixed point iteration\n", + " error = np.max(np.abs((G_tau[\"up\"].data[:,0,0] - G_old[\"up\"].data[:,0,0]))) # Compute absolute error\n", + " iter += 1\n", + "\n", + " # Print iteration number and error\n", + " print(\"Iteration:\", iter, \"Error:\", error)\n", + " if iter > params[\"max_iter\"]:\n", + " print(\"Maximum number of iterations reached without convergence\")\n", + " break" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "c0669c9e", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "G_tau_dense = make_gf_imtime(G_tau[\"up\"], n_tau=1000) # Obtain DLR expansion on dense imaginary time grid\n", + "t = np.array([x.real for x in G_tau_dense.mesh.values()])[1:] # Obtain dense grid\n", + "Gconformal = -np.pi**(1/4) / np.sqrt(2*params[\"beta\"]) * 1/np.sqrt(np.sin(np.pi * t / params[\"beta\"])) # Conformal solution\n", + "\n", + "plt.figure(figsize = (10,10))\n", + "oplot(G_tau_dense.real, label = r\"$\\mathrm{Re}\\, G(\\tau)$ (DLR)\")\n", + "oplot(G_tau[\"up\"].real, marker = \"o\", markeredgecolor = \"black\", label = r\"$\\mathrm{Re}\\, G(\\tau)$ (DLR nodes)\")\n", + "plt.plot(t, Gconformal, label = r\"$G_c(\\tau)$\", color = \"red\", linestyle = \"dashed\")\n", + "plt.ylim(-0.5,0)\n", + "plt.ylabel(\"\")\n", + "plt.legend(loc=\"upper left\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "f76bdb41-bb7f-4aea-8061-ec627d77e4dd", + "metadata": { + "tags": [] + }, + "source": [ + "Note that in this case, the Green's function is purely real. We observe a slight discrepancy with the conformal solution at the endpoints (which is expected---see the reference). You can experiment with increasing $\\beta$ (it might be necessary to increase the mixing parameter $\\alpha$ in order to converge), and should observe even closer agreement with the conformal solution. We can also plot the self-energy in Matsubara frequency, which is purely imaginary:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "f728e5fc", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "Sigma_iw_dense = make_gf_imfreq(Sigma_iw[\"up\"], n_iw = 5000) # Obtain DLR expansion on dense Matsubara frequency grid\n", + "\n", + "plt.figure(figsize = (10,10))\n", + "oplot(Sigma_iw_dense.imag, marker = \"o\", markeredgecolor = \"red\", markersize=2, linestyle=\"none\", label = r\"Im $\\Sigma(i \\omega_n)$ (DLR)\")\n", + "plt.xlim(-30,30)\n", + "plt.ylabel(\"\")\n", + "plt.show()" + ] + } + ], + "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": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}