{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "scrolled": true }, "outputs": [], "source": [ "import gpt as g\n", "import matplotlib.pyplot as plt\n", "import numpy as np" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Lecture 3: A first look at the QCD module. We generate a quenched ensemble, measure the wilson flow scale and compute a domain-wall pion correlator." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We start by creating a $8^3 \\times 32$ double precision grid." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "grid = g.grid([8, 8, 8, 32], g.double)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we create a parallel pseudorandom number generator and a unit gauge configuration." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "GPT : 0.695516 s : Initializing gpt.random(test,vectorized_ranlux24_389_64) took 0.000295162 s\n" ] } ], "source": [ "rng = g.random(\"test\")\n", "U = g.qcd.gauge.unit(grid)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The gauge field is a list of color matrices, currently initialized to unit matrices." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "GPT : 0.739074 s : We live in 4 space-time dimensions\n", "GPT : 0.743269 s : U[0][0,0,0,0] = tensor([[1.+0.j 0.+0.j 0.+0.j]\n", " : [0.+0.j 1.+0.j 0.+0.j]\n", " : [0.+0.j 0.+0.j 1.+0.j]],ot_matrix_su_n_fundamental_group(3))\n" ] } ], "source": [ "Nd = len(U)\n", "g.message(f\"We live in {Nd} space-time dimensions\")\n", "g.message(f\"U[0][0,0,0,0] = {U[0][0,0,0,0]}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we will prepare for applying a SU$(2)$ subgroup heatbath algorithm to generate an ensemble of quenched QCD configurations. A reasonable updating scheme, first updates the even and then the odd sites. So we need helper fields to mask these subsets." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "grid_eo = grid.checkerboarded(g.redblack)\n", "mask_rb = g.complex(grid_eo)\n", "mask_rb[:] = 1\n", "mask = g.complex(grid)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us now generate a pure Wilson gauge ensemble with $\\beta=5.5$. For this, we first define a staple and the parameter." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# gauge action parameter\n", "beta = 5.5\n", "\n", "# simple plaquette action\n", "def staple(U, mu):\n", " st = g.lattice(U[0])\n", " st[:] = 0\n", " Nd = len(U)\n", " for nu in range(Nd):\n", " if mu != nu:\n", " st += beta * g.qcd.gauge.staple(U, mu, nu) / U[0].otype.Nc\n", " return st" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "GPT : 1.228672 s : SU(2)-subgroup heatbath 0 has P = 1.0, R_2x1 = 1.0\n", "GPT : 2.024035 s : SU(2)-subgroup heatbath 1 has P = 0.6690106656133712, R_2x1 = 0.49840042565202697\n", "GPT : 3.018548 s : SU(2)-subgroup heatbath 2 has P = 0.597529950168559, R_2x1 = 0.3989602320643259\n", "GPT : 3.768288 s : SU(2)-subgroup heatbath 3 has P = 0.574074009187597, R_2x1 = 0.3651939333922672\n", "GPT : 4.527717 s : SU(2)-subgroup heatbath 4 has P = 0.560211411679096, R_2x1 = 0.3453226269277517\n", "GPT : 5.288741 s : SU(2)-subgroup heatbath 5 has P = 0.5512347885669554, R_2x1 = 0.3330227490132814\n", "GPT : 6.078276 s : SU(2)-subgroup heatbath 6 has P = 0.5448459886651085, R_2x1 = 0.324675311762747\n", "GPT : 6.851558 s : SU(2)-subgroup heatbath 7 has P = 0.5414547577156111, R_2x1 = 0.32047505366100904\n", "GPT : 7.593363 s : SU(2)-subgroup heatbath 8 has P = 0.5389550422162213, R_2x1 = 0.3170285207906144\n", "GPT : 8.623147 s : SU(2)-subgroup heatbath 9 has P = 0.5374028782315653, R_2x1 = 0.3148905439777856\n", "GPT : 9.447113 s : SU(2)-subgroup heatbath 10 has P = 0.5346290039127525, R_2x1 = 0.31128812960212787\n", "GPT : 10.436505 s : SU(2)-subgroup heatbath 11 has P = 0.5335921326134159, R_2x1 = 0.3092732942993306\n", "GPT : 11.184879 s : SU(2)-subgroup heatbath 12 has P = 0.5322874688256605, R_2x1 = 0.3067926555637845\n", "GPT : 11.944969 s : SU(2)-subgroup heatbath 13 has P = 0.5289926204991453, R_2x1 = 0.30206944240221584\n", "GPT : 12.671803 s : SU(2)-subgroup heatbath 14 has P = 0.5267403945504542, R_2x1 = 0.2998278636738912\n", "GPT : 13.415984 s : SU(2)-subgroup heatbath 15 has P = 0.5248440111427469, R_2x1 = 0.29759322488045614\n", "GPT : 14.147916 s : SU(2)-subgroup heatbath 16 has P = 0.5237313830199323, R_2x1 = 0.2959462786558421\n", "GPT : 14.878366 s : SU(2)-subgroup heatbath 17 has P = 0.5229207928588373, R_2x1 = 0.29452963806969384\n", "GPT : 15.615127 s : SU(2)-subgroup heatbath 18 has P = 0.522696440738225, R_2x1 = 0.2943754103936752\n", "GPT : 16.365320 s : SU(2)-subgroup heatbath 19 has P = 0.5223392247506009, R_2x1 = 0.293905686835285\n", "GPT : 17.099310 s : SU(2)-subgroup heatbath 20 has P = 0.521622390252707, R_2x1 = 0.2918027788743217\n", "GPT : 18.136739 s : SU(2)-subgroup heatbath 21 has P = 0.5207595962025382, R_2x1 = 0.29020020461811985\n", "GPT : 18.935207 s : SU(2)-subgroup heatbath 22 has P = 0.5197337784830696, R_2x1 = 0.2903676008363169\n", "GPT : 19.834952 s : SU(2)-subgroup heatbath 23 has P = 0.5196708381955242, R_2x1 = 0.2893722193465197\n", "GPT : 20.571369 s : SU(2)-subgroup heatbath 24 has P = 0.5172227366628478, R_2x1 = 0.28764029959777815\n", "GPT : 21.327653 s : SU(2)-subgroup heatbath 25 has P = 0.5163534180788868, R_2x1 = 0.2855787360096612\n", "GPT : 22.057558 s : SU(2)-subgroup heatbath 26 has P = 0.5156672373752595, R_2x1 = 0.28427126422122473\n", "GPT : 22.801172 s : SU(2)-subgroup heatbath 27 has P = 0.5150003650073259, R_2x1 = 0.2827392523848131\n", "GPT : 23.526807 s : SU(2)-subgroup heatbath 28 has P = 0.5129433190441942, R_2x1 = 0.28126153213922284\n", "GPT : 24.264430 s : SU(2)-subgroup heatbath 29 has P = 0.5116990438100496, R_2x1 = 0.27846178087802576\n", "GPT : 24.987112 s : SU(2)-subgroup heatbath 30 has P = 0.5107232765956586, R_2x1 = 0.276371440677104\n", "GPT : 25.740191 s : SU(2)-subgroup heatbath 31 has P = 0.5104954920221523, R_2x1 = 0.27753305718295457\n", "GPT : 26.528184 s : SU(2)-subgroup heatbath 32 has P = 0.510675469060811, R_2x1 = 0.2770174565263681\n", "GPT : 27.271163 s : SU(2)-subgroup heatbath 33 has P = 0.5093600611721335, R_2x1 = 0.2750674462376038\n", "GPT : 28.071553 s : SU(2)-subgroup heatbath 34 has P = 0.508258535389119, R_2x1 = 0.27434614594675055\n", "GPT : 28.859199 s : SU(2)-subgroup heatbath 35 has P = 0.507133402340208, R_2x1 = 0.27217798932503223\n", "GPT : 29.837528 s : SU(2)-subgroup heatbath 36 has P = 0.5071350034686778, R_2x1 = 0.2724485086211964\n", "GPT : 30.874124 s : SU(2)-subgroup heatbath 37 has P = 0.5068700169881849, R_2x1 = 0.2713917371136818\n", "GPT : 31.657547 s : SU(2)-subgroup heatbath 38 has P = 0.5058852052461333, R_2x1 = 0.2712790883936668\n", "GPT : 32.412842 s : SU(2)-subgroup heatbath 39 has P = 0.503528049444319, R_2x1 = 0.26874729714943285\n", "GPT : 33.361245 s : SU(2)-subgroup heatbath 40 has P = 0.5038801871873279, R_2x1 = 0.2683416894727666\n", "GPT : 34.408417 s : SU(2)-subgroup heatbath 41 has P = 0.5042787378833202, R_2x1 = 0.2675935089260387\n", "GPT : 35.498497 s : SU(2)-subgroup heatbath 42 has P = 0.5037351923543592, R_2x1 = 0.2677337199461232\n", "GPT : 36.352854 s : SU(2)-subgroup heatbath 43 has P = 0.5038612451680923, R_2x1 = 0.26768706967361106\n", "GPT : 37.451407 s : SU(2)-subgroup heatbath 44 has P = 0.5034777427699275, R_2x1 = 0.26815612446618575\n", "GPT : 38.340764 s : SU(2)-subgroup heatbath 45 has P = 0.5037059087709117, R_2x1 = 0.2678297229612208\n", "GPT : 39.106971 s : SU(2)-subgroup heatbath 46 has P = 0.5010009073386555, R_2x1 = 0.26541783949446096\n", "GPT : 39.885660 s : SU(2)-subgroup heatbath 47 has P = 0.5001107162914609, R_2x1 = 0.26496104483417804\n", "GPT : 40.641190 s : SU(2)-subgroup heatbath 48 has P = 0.5011764112780589, R_2x1 = 0.264529416146723\n", "GPT : 41.390055 s : SU(2)-subgroup heatbath 49 has P = 0.5004521646397174, R_2x1 = 0.2633316834071487\n", "GPT : 42.110440 s : SU(2)-subgroup heatbath 50 has P = 0.4988889262706495, R_2x1 = 0.26248699250570195\n", "GPT : 42.848295 s : SU(2)-subgroup heatbath 51 has P = 0.4988854325457215, R_2x1 = 0.26233033624039426\n", "GPT : 43.595043 s : SU(2)-subgroup heatbath 52 has P = 0.4969800914351901, R_2x1 = 0.26058425022109866\n", "GPT : 44.416473 s : SU(2)-subgroup heatbath 53 has P = 0.4998628601084023, R_2x1 = 0.2625900905483684\n", "GPT : 45.433482 s : SU(2)-subgroup heatbath 54 has P = 0.4986233193331487, R_2x1 = 0.2615525935176275\n", "GPT : 46.447440 s : SU(2)-subgroup heatbath 55 has P = 0.4979573497220633, R_2x1 = 0.2606588941981954\n", "GPT : 47.329072 s : SU(2)-subgroup heatbath 56 has P = 0.49781489516018546, R_2x1 = 0.2602806680846015\n", "GPT : 48.100114 s : SU(2)-subgroup heatbath 57 has P = 0.49901263569375076, R_2x1 = 0.2622087306900958\n", "GPT : 48.853377 s : SU(2)-subgroup heatbath 58 has P = 0.4982848857069518, R_2x1 = 0.2610435965162297\n", "GPT : 49.604964 s : SU(2)-subgroup heatbath 59 has P = 0.496629893900633, R_2x1 = 0.25975525861010385\n", "GPT : 50.362492 s : SU(2)-subgroup heatbath 60 has P = 0.4972276644175322, R_2x1 = 0.26096046534213724\n", "GPT : 51.122295 s : SU(2)-subgroup heatbath 61 has P = 0.4973653239203925, R_2x1 = 0.26066888523890774\n", "GPT : 51.852557 s : SU(2)-subgroup heatbath 62 has P = 0.49781950135353603, R_2x1 = 0.26024677415702807\n", "GPT : 52.743349 s : SU(2)-subgroup heatbath 63 has P = 0.4965946174263427, R_2x1 = 0.2593583209868893\n", "GPT : 53.745219 s : SU(2)-subgroup heatbath 64 has P = 0.4975634372403866, R_2x1 = 0.2605399742451014\n", "GPT : 54.508461 s : SU(2)-subgroup heatbath 65 has P = 0.4974333065379764, R_2x1 = 0.26090502201659255\n", "GPT : 55.498797 s : SU(2)-subgroup heatbath 66 has P = 0.4978085473625, R_2x1 = 0.260605879326538\n", "GPT : 56.274074 s : SU(2)-subgroup heatbath 67 has P = 0.4966137086346479, R_2x1 = 0.25845505801415275\n", "GPT : 57.027054 s : SU(2)-subgroup heatbath 68 has P = 0.4983371306437385, R_2x1 = 0.26290473931920305\n", "GPT : 57.758389 s : SU(2)-subgroup heatbath 69 has P = 0.5006811632224762, R_2x1 = 0.26325350603636727\n", "GPT : 58.507140 s : SU(2)-subgroup heatbath 70 has P = 0.5006054279535769, R_2x1 = 0.26440028202070176\n", "GPT : 59.259306 s : SU(2)-subgroup heatbath 71 has P = 0.4999829283642152, R_2x1 = 0.26259430336586276\n", "GPT : 60.008251 s : SU(2)-subgroup heatbath 72 has P = 0.5014474917596622, R_2x1 = 0.265227741560201\n", "GPT : 60.757097 s : SU(2)-subgroup heatbath 73 has P = 0.4998487522366511, R_2x1 = 0.26352821847388863\n", "GPT : 61.505800 s : SU(2)-subgroup heatbath 74 has P = 0.5015949730285314, R_2x1 = 0.2645436623650712\n", "GPT : 62.234760 s : SU(2)-subgroup heatbath 75 has P = 0.5009047622633881, R_2x1 = 0.26322131257196335\n", "GPT : 62.975199 s : SU(2)-subgroup heatbath 76 has P = 0.4990510773752887, R_2x1 = 0.2627908008657167\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "GPT : 63.711681 s : SU(2)-subgroup heatbath 77 has P = 0.4988943200994418, R_2x1 = 0.26234017632122436\n", "GPT : 64.460567 s : SU(2)-subgroup heatbath 78 has P = 0.4990565364723418, R_2x1 = 0.26275856334032516\n", "GPT : 65.205037 s : SU(2)-subgroup heatbath 79 has P = 0.5001406479881055, R_2x1 = 0.26397745448997223\n", "GPT : 65.943483 s : SU(2)-subgroup heatbath 80 has P = 0.4996786317077962, R_2x1 = 0.26318061582624286\n", "GPT : 66.685377 s : SU(2)-subgroup heatbath 81 has P = 0.4987926866663753, R_2x1 = 0.2624054602526124\n", "GPT : 67.428747 s : SU(2)-subgroup heatbath 82 has P = 0.4982065830637969, R_2x1 = 0.2607413427661306\n", "GPT : 68.168230 s : SU(2)-subgroup heatbath 83 has P = 0.49759479874287593, R_2x1 = 0.26046806133127076\n", "GPT : 68.905076 s : SU(2)-subgroup heatbath 84 has P = 0.49587414167832694, R_2x1 = 0.25895552394334154\n", "GPT : 69.649296 s : SU(2)-subgroup heatbath 85 has P = 0.4979953837991206, R_2x1 = 0.2620148450232836\n", "GPT : 70.393859 s : SU(2)-subgroup heatbath 86 has P = 0.49792984719434497, R_2x1 = 0.26094313457109863\n", "GPT : 71.152666 s : SU(2)-subgroup heatbath 87 has P = 0.49611864123511934, R_2x1 = 0.2594023786921903\n", "GPT : 71.905763 s : SU(2)-subgroup heatbath 88 has P = 0.49755915458297156, R_2x1 = 0.26020335634318553\n", "GPT : 72.648205 s : SU(2)-subgroup heatbath 89 has P = 0.4991158117017116, R_2x1 = 0.2619766386934485\n", "GPT : 73.400997 s : SU(2)-subgroup heatbath 90 has P = 0.499417264497759, R_2x1 = 0.26295041846887823\n", "GPT : 74.137281 s : SU(2)-subgroup heatbath 91 has P = 0.49944276993337616, R_2x1 = 0.262395482784557\n", "GPT : 74.878008 s : SU(2)-subgroup heatbath 92 has P = 0.49722405019908283, R_2x1 = 0.2609044785201382\n", "GPT : 75.629620 s : SU(2)-subgroup heatbath 93 has P = 0.4961598649332088, R_2x1 = 0.2589275615710526\n", "GPT : 76.375088 s : SU(2)-subgroup heatbath 94 has P = 0.4972402474925503, R_2x1 = 0.2585345826221943\n", "GPT : 77.133587 s : SU(2)-subgroup heatbath 95 has P = 0.49709766938126343, R_2x1 = 0.2609900736606732\n", "GPT : 77.861890 s : SU(2)-subgroup heatbath 96 has P = 0.4966586695359743, R_2x1 = 0.2593884120979422\n", "GPT : 78.611163 s : SU(2)-subgroup heatbath 97 has P = 0.49608929416079, R_2x1 = 0.2582838724966286\n", "GPT : 79.361185 s : SU(2)-subgroup heatbath 98 has P = 0.49788924303315024, R_2x1 = 0.26047361742183733\n", "GPT : 80.130467 s : SU(2)-subgroup heatbath 99 has P = 0.49884036532568005, R_2x1 = 0.2606411660205475\n" ] } ], "source": [ "g.default.push_verbose(\"su2_heat_bath\", False) # disable verbose algorithm\n", "\n", "markov = g.algorithms.markov.su2_heat_bath(rng)\n", "\n", "for it in range(100):\n", " plaq = g.qcd.gauge.plaquette(U)\n", " R_2x1 = g.qcd.gauge.rectangle(U, 2, 1)\n", " g.message(f\"SU(2)-subgroup heatbath {it} has P = {plaq}, R_2x1 = {R_2x1}\")\n", " for cb in [g.even, g.odd]:\n", " mask[:] = 0\n", " mask_rb.checkerboard(cb)\n", " g.set_checkerboard(mask, mask_rb)\n", "\n", " for mu in range(Nd):\n", " st = g.eval(staple(U, mu))\n", " markov(U[mu], st, mask)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now save the current gauge configuration to a file." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Grid : Message : 80.790184 s : IOobject: C++ write I/O /notebooks/ckpoint.lat : 9437184 bytes and offset 571\n", "Grid : Message : 80.821321 s : IOobject: write 9437184 bytes in 0.031154 s 288.887 MB/s \n", "Grid : Message : 80.821343 s : IOobject: endian and checksum overhead 0.001471 s\n", "Grid : Message : 80.821352 s : writeLatticeObject: unvectorize overhead 0.001286 s\n", "Grid : Message : 80.833499 s : Written NERSC Configuration on /notebooks/ckpoint.lat checksum d1f8047c plaq 0.49813\n" ] } ], "source": [ "g.save(\"/notebooks/ckpoint.lat\", U, g.format.nersc())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For completeness, here is how we would load a gauge configuration:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Grid : Message : 80.846075 s : GPT::IO: gdimension[0] = 8\n", "Grid : Message : 80.846091 s : GPT::IO: gdimension[1] = 8\n", "Grid : Message : 80.846098 s : GPT::IO: gdimension[2] = 8\n", "Grid : Message : 80.846106 s : GPT::IO: gdimension[3] = 32\n", "Grid : Message : 80.846856 s : * BEGIN_HEADER\n", "Grid : Message : 80.846902 s : * HDR_VERSION = \n", "Grid : Message : 80.846910 s : * DATATYPE = 4D_SU3_GAUGE_3x3\n", "Grid : Message : 80.846920 s : * STORAGE_FORMAT = \n", "Grid : Message : 80.846926 s : * DIMENSION_1 = 8\n", "Grid : Message : 80.846935 s : * DIMENSION_2 = 8\n", "Grid : Message : 80.846945 s : * DIMENSION_3 = 8\n", "Grid : Message : 80.846952 s : * DIMENSION_4 = 32\n", "Grid : Message : 80.846963 s : * LINK_TRACE = -0.00047949944\n", "Grid : Message : 80.846971 s : * PLAQUETTE = 0.4981299962\n", "Grid : Message : 80.846982 s : * BOUNDARY_1 = PERIODIC\n", "Grid : Message : 80.846996 s : * BOUNDARY_2 = PERIODIC\n", "Grid : Message : 80.847000 s : * BOUNDARY_3 = PERIODIC\n", "Grid : Message : 80.847005 s : * BOUNDARY_4 = PERIODIC\n", "Grid : Message : 80.847010 s : * CHECKSUM = d1f8047c\n", "Grid : Message : 80.847018 s : * SCIDAC_CHECKSUMA = 0\n", "Grid : Message : 80.847026 s : * SCIDAC_CHECKSUMB = 0\n", "Grid : Message : 80.847031 s : * ENSEMBLE_ID = UKQCD\n", "Grid : Message : 80.847038 s : * ENSEMBLE_LABEL = DWF\n", "Grid : Message : 80.847045 s : * SEQUENCE_NUMBER = 1\n", "Grid : Message : 80.847190 s : * CREATOR = gpt\n", "Grid : Message : 80.847196 s : * CREATOR_HARDWARE = a19eaa8d4492-x86_64-Linux-5.10.25-linuxkit\n", "Grid : Message : 80.847203 s : * CREATION_DATE = \n", "Grid : Message : 80.847209 s : * ARCHIVE_DATE = \n", "Grid : Message : 80.847226 s : * FLOATING_POINT = IEEE64BIG\n", "Grid : Message : 80.847234 s : * END_HEADER\n", "Grid : Message : 80.848484 s : IOobject: C++ read I/O /notebooks/ckpoint.lat : 9437184 bytes and offset 571\n", "Grid : Message : 80.910667 s : IOobject: read 9437184 bytes in 0.051105 s 176.108 MB/s \n", "Grid : Message : 80.910715 s : IOobject: endian and checksum overhead 0.011076 s\n", "Grid : Message : 80.913557 s : readLatticeObject: vectorize overhead 0.002820 s\n", "Grid : Message : 80.926271 s : NERSC Configuration /notebooks/ckpoint.lat checksum d1f8047c header d1f8047c\n", "Grid : Message : 80.926290 s : NERSC Configuration /notebooks/ckpoint.lat plaquette 0.49813 header 0.49813\n", "Grid : Message : 80.926311 s : NERSC Configuration /notebooks/ckpoint.lat link_trace -0.000479499 header -0.000479499\n", "Grid : Message : 80.926322 s : NERSC Configuration /notebooks/ckpoint.lat and plaquette, link trace, and checksum agree\n" ] } ], "source": [ "Uprime = g.load(\"/notebooks/ckpoint.lat\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, let us smear the gauge field using the Wilson flow and a fourth-order Runge-Kutta scheme:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "GPT : 81.320474 s : t^2 E(t=0.05)=0.005810520748364589\n", "GPT : 81.592873 s : t^2 E(t=0.1)=0.02174229379848457\n", "GPT : 81.866448 s : t^2 E(t=0.15)=0.04493423745983812\n", "GPT : 82.126579 s : t^2 E(t=0.2)=0.07285409659909867\n", "GPT : 82.387142 s : t^2 E(t=0.25)=0.10378780682326139\n", "GPT : 82.645226 s : t^2 E(t=0.3)=0.1367131480345164\n", "GPT : 82.897213 s : t^2 E(t=0.35)=0.17105448048020502\n", "GPT : 83.157549 s : t^2 E(t=0.4)=0.20649231431253923\n", "GPT : 83.408843 s : t^2 E(t=0.45)=0.24284421848087684\n", "GPT : 83.664786 s : t^2 E(t=0.5)=0.2799961091006515\n", "GPT : 83.916811 s : t^2 E(t=0.55)=0.3178636509857205\n", "GPT : 84.183352 s : t^2 E(t=0.6)=0.35637195185484694\n", "GPT : 84.434624 s : t^2 E(t=0.65)=0.3954467115073493\n", "GPT : 84.672887 s : t^2 E(t=0.7)=0.43501155876736153\n", "GPT : 84.928478 s : t^2 E(t=0.75)=0.47498750077044555\n" ] } ], "source": [ "t = 0.0\n", "eps = 0.05\n", "U_wf = g.copy(U)\n", "plot_x = []\n", "plot_y = []\n", "for i in range(15):\n", " U_wf = g.qcd.gauge.smear.wilson_flow(U_wf, epsilon=eps)\n", " t += eps\n", " E = g.qcd.gauge.energy_density(U_wf)\n", " g.message(f\"t^2 E(t={t:g})={t**2. * E}\")\n", " plot_x.append(t)\n", " plot_y.append(t**2. * E)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use this to approximately set a scale for this ensemble:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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n9/YwO/RyC3BZ3hS9EniU0X+bNm6AvHiLY/+O5d4UnVkr8HJGN3T2D+HcTtYJ/C6jVa92ZK2bjv88y70pOs+5/eWJ178HPLCDaz0IfHT8+lpGlzyev1PrHR/3IuAs4wmZO/Fr6QUs6S/wtxmNCL4FHBvvu4fRCBfglYxGEP/LaLHr0zu41n8F/gt4aPx1coef278ETo9r/dylQnTZtW46dqmBPue5/fPxuf3q+Ny+aAfXGkaXtB4Gvg4c3snndrz9Z8BfLLPOWV9O/ZekRlyO19AlqUkGuiQ1wkCXpEYY6JLUCANdkhphoEtSIwx0SWrE/wP4Lqq/HgY5MAAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "GPT : 85.028145 s : Lattice scale is approximately: 0.94 GeV\n" ] } ], "source": [ "plt.plot(plot_x, plot_y, 'ro')\n", "plt.show()\n", "\n", "t0_over_asqr = 0.525\n", "ainvOverGeV = 1.3 * t0_over_asqr**0.5 # live in world with t0^-1/2 = 1.3 GeV\n", "g.message(f\"Lattice scale is approximately: {ainvOverGeV:.2g} GeV\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let us prepare a mobius domain-wall fermion on this gauge configuration." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "qm = g.qcd.fermion.mobius(U, {\n", " \"mass\": 0.12,\n", " \"M5\": 1.8,\n", " \"b\": 1.5,\n", " \"c\": 0.5,\n", " \"Ls\": 12,\n", " \"boundary_phases\": [1.0, 1.0, 1.0, -1.0],\n", "})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Create a physical four-dimensional propagator using a simple even-odd preconditioned solver." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "pc = g.qcd.fermion.preconditioner\n", "inv = g.algorithms.inverter\n", "\n", "g.default.push_verbose(\"cg_convergence\", True) # want to see CG progress\n", "Q = qm.propagator(inv.preconditioned(pc.eo2_ne(), inv.cg({\"eps\": 1e-6, \"maxiter\": 100}))).grouped(1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, let us create a point source at the origin and create a propagator field." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "GPT : 85.582798 s : cg: iteration 0: 1.584105e-01 / 1.004914e-12\n", "GPT : 85.636232 s : cg: iteration 1: 5.392260e-02 / 1.004914e-12\n", "GPT : 85.701626 s : cg: iteration 2: 2.842069e-02 / 1.004914e-12\n", "GPT : 85.759671 s : cg: iteration 3: 1.582130e-02 / 1.004914e-12\n", "GPT : 85.820299 s : cg: iteration 4: 9.292336e-03 / 1.004914e-12\n", "GPT : 85.881978 s : cg: iteration 5: 6.019122e-03 / 1.004914e-12\n", "GPT : 85.945778 s : cg: iteration 6: 4.171264e-03 / 1.004914e-12\n", "GPT : 86.018681 s : cg: iteration 7: 3.077872e-03 / 1.004914e-12\n", "GPT : 86.115801 s : cg: iteration 8: 2.304801e-03 / 1.004914e-12\n", "GPT : 86.204624 s : cg: iteration 9: 1.800294e-03 / 1.004914e-12\n", "GPT : 86.297794 s : cg: iteration 10: 1.440302e-03 / 1.004914e-12\n", "GPT : 86.385984 s : cg: iteration 11: 1.156532e-03 / 1.004914e-12\n", "GPT : 86.469620 s : cg: iteration 12: 9.395925e-04 / 1.004914e-12\n", "GPT : 86.554053 s : cg: iteration 13: 7.911396e-04 / 1.004914e-12\n", "GPT : 86.639154 s : cg: iteration 14: 6.887446e-04 / 1.004914e-12\n", "GPT : 86.724674 s : cg: iteration 15: 5.911933e-04 / 1.004914e-12\n", "GPT : 86.808558 s : cg: iteration 16: 5.160909e-04 / 1.004914e-12\n", "GPT : 86.884715 s : cg: iteration 17: 4.650508e-04 / 1.004914e-12\n", "GPT : 86.954744 s : cg: iteration 18: 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1.003176e-12\n" ] } ], "source": [ "src = g.mspincolor(grid)\n", "g.create.point(src, [0, 1, 0, 0])\n", "\n", "prop_field = g.eval( Q * src )" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "corr = g.slice(g.trace(prop_field * g.adj(prop_field)),3)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "E_mass = [np.log(corr[t]/corr[t+1]).real for t in range(16)]" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(range(16), E_mass, 'ro')\n", "plt.ylim(0,2)\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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 }