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738 lines
34 KiB
738 lines
34 KiB
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"# use numpy number of threads one\n",
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"# print(threadpool_info())\n",
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"# from threadpoolctl import threadpool_info, threadpool_limits\n",
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"# user_api = threadpool_info()[0][\"user_api\"]\n",
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"# threadpool_limits(limits=1, user_api=user_api)\n",
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"# print(threadpool_info())"
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]
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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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"metadata": {},
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"outputs": [
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"info:0: SislInfo: Please install tqdm (pip install tqdm) for better looking progress bars\n"
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]
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"0.14.3\n",
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"1.24.4\n"
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"[Daniels-Air:00184] shmem: mmap: an error occurred while determining whether or not /var/folders/yh/dx7xl94n3g52ts3td8qcxjcc0000gn/T//ompi.Daniels-Air.501/jf.0/273678336/sm_segment.Daniels-Air.501.10500000.0 could be created.\n"
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]
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}
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],
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"source": [
|
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"from sys import getsizeof\n",
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"from timeit import default_timer as timer\n",
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"\n",
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"import sisl\n",
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"from src.grogupy import *\n",
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"from mpi4py import MPI\n",
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"import warnings\n",
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"\n",
|
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"# runtime information\n",
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"times = dict()\n",
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"times[\"start_time\"] = timer()\n",
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"########################\n",
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"# it works if data is in downloads folder\n",
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"########################\n",
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"sisl.__version__\n",
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"\n",
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"try:\n",
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" print(sisl.__version__)\n",
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"except:\n",
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" print(\"sisl version unknown.\")\n",
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"\n",
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"try:\n",
|
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" print(np.__version__)\n",
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"except:\n",
|
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" print(\"numpy version unknown.\")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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"ename": "TypeError",
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"evalue": "'NoneType' object is not iterable",
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"output_type": "error",
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"traceback": [
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"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
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"\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)",
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"Cell \u001b[0;32mIn[58], line 28\u001b[0m\n\u001b[1;32m 26\u001b[0m magnetic_entities \u001b[38;5;241m=\u001b[39m fdf\u001b[38;5;241m.\u001b[39mget(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mMagneticEntities\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m 27\u001b[0m fdf_magnetic_entities \u001b[38;5;241m=\u001b[39m []\n\u001b[0;32m---> 28\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m mag_ent \u001b[38;5;129;01min\u001b[39;00m magnetic_entities:\n\u001b[1;32m 29\u001b[0m row \u001b[38;5;241m=\u001b[39m mag_ent\u001b[38;5;241m.\u001b[39msplit()\n\u001b[1;32m 30\u001b[0m dat \u001b[38;5;241m=\u001b[39m []\n",
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"\u001b[0;31mTypeError\u001b[0m: 'NoneType' object is not iterable"
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]
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}
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],
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"source": [
|
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"# open fdf input\n",
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"fdf = sisl.io.fdfSileSiesta(\"input.fdf\")\n",
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"\n",
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"fdf_parameters = dict()\n",
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"fdf_parameters[\"infile\"] = fdf.get(\"InputFile\")\n",
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"fdf_parameters[\"outfile\"] = fdf.get(\"OutputFile\")\n",
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"fdf_parameters[\"scf_xcf_orientation\"] = np.array(fdf.get(\"ScfXcfOrientation\"))\n",
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"\n",
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"rotations = fdf.get(\"XCF_Rotation\")\n",
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"if rotations is None:\n",
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" pass\n",
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"else:\n",
|
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" fdf_rot = []\n",
|
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" for rot in rotations:\n",
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" dat = np.array(rot.split()[:9], dtype=float)\n",
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" o = dat[:3]\n",
|
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" vw = dat[3:]\n",
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" vw = vw.reshape(2, 3)\n",
|
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" fdf_rot.append(dict(o=o, vw=vw))\n",
|
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" fdf_parameters[\"ref_xcf_orientations\"] = fdf_rot\n",
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"\n",
|
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"pairs = fdf.get(\"Pairs\")\n",
|
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"if pairs in None:\n",
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" pass\n",
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"else:\n",
|
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" fdf_pairs = []\n",
|
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" for fdf_pair in pairs:\n",
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" dat = np.array(fdf_pair.split()[:5], dtype=int)\n",
|
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" my_pair = dict(ai=dat[0], aj=dat[1], Ruc=np.array(dat[2:]))\n",
|
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" fdf_pairs.append(my_pair)\n",
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"\n",
|
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"magnetic_entities = fdf.get(\"MagneticEntities\")\n",
|
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"if magnetic_entities is None:\n",
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" pass\n",
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"else:\n",
|
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" fdf_magnetic_entities = []\n",
|
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" for mag_ent in magnetic_entities:\n",
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" row = mag_ent.split()\n",
|
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" dat = []\n",
|
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" for string in row:\n",
|
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" if string.find(\"#\") != -1:\n",
|
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" break\n",
|
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" dat.append(string)\n",
|
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" if dat[0] == \"Cluster\" or \"cluster\":\n",
|
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" fdf_magnetic_entities.append(dict(atom=dat[1:]))\n",
|
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" continue\n",
|
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" elif dat[0] == \"AtomShell\" or \"Atomshell\" or \"atomShell\" or \"atomshell\":\n",
|
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" fdf_magnetic_entities.append(dict(atom=dat[1], l=dat[2:]))\n",
|
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" continue\n",
|
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" elif dat[0] == \"AtomOrbital\" or \"Atomorbital\" or \"tomOrbital\" or \"atomorbital\":\n",
|
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" continue\n",
|
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" elif dat[0] == \"Orbitals\" or \"orbitals\":\n",
|
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" continue\n",
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" else:\n",
|
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" print(\"Unrecognizable magnetic entity in fdf\")\n",
|
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" break\n",
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"\n",
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"\n",
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"fdf_parameters[\"kset\"] = fdf.get(\"INTEGRAL.Kset\")\n",
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"fdf_parameters[\"kdirs\"] = fdf.get(\"INTEGRAL.Kdirs\")\n",
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"fdf_parameters[\"ebot\"] = fdf.get(\"INTEGRAL.Ebot\")\n",
|
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"fdf_parameters[\"eset\"] = fdf.get(\"INTEGRAL.Eset\")\n",
|
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"fdf_parameters[\"esetp\"] = fdf.get(\"INTEGRAL.Esetp\")\n",
|
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"fdf_parameters[\"parallel_solver_for_Gk\"] = fdf.get(\"GREEN.ParallelSolver\")\n",
|
|
"fdf_parameters[\"padawan_mode\"] = fdf.get(\"PadawanMode\")"
|
|
]
|
|
},
|
|
{
|
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"cell_type": "code",
|
|
"execution_count": null,
|
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"metadata": {},
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"outputs": [],
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"source": []
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},
|
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{
|
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"cell_type": "code",
|
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"execution_count": 4,
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"metadata": {},
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"outputs": [],
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"source": [
|
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"################################################################################\n",
|
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"#################################### INPUT #####################################\n",
|
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"################################################################################\n",
|
|
"path = (\n",
|
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" \"/Users/danielpozsar/Downloads/nojij/Fe3GeTe2/monolayer/soc/lat3_791/Fe3GeTe2.fdf\"\n",
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")\n",
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"outfile = \"./Fe3GeTe2_notebook\"\n",
|
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"\n",
|
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"# this information needs to be given at the input!!\n",
|
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"scf_xcf_orientation = np.array([0, 0, 1]) # z\n",
|
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"# list of reference directions for around which we calculate the derivatives\n",
|
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"# o is the quantization axis, v and w are two axes perpendicular to it\n",
|
|
"# at this moment the user has to supply o,v,w on the input.\n",
|
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"# we can have some default for this\n",
|
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"ref_xcf_orientations = [\n",
|
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" dict(o=np.array([1, 0, 0]), vw=[np.array([0, 1, 0]), np.array([0, 0, 1])]),\n",
|
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" dict(o=np.array([0, 1, 0]), vw=[np.array([1, 0, 0]), np.array([0, 0, 1])]),\n",
|
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" dict(o=np.array([0, 0, 1]), vw=[np.array([1, 0, 0]), np.array([0, 1, 0])]),\n",
|
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"]\n",
|
|
"magnetic_entities = [\n",
|
|
" dict(atom=3, l=2),\n",
|
|
" dict(atom=4, l=2),\n",
|
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" dict(atom=5, l=2),\n",
|
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"]\n",
|
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"pairs = [\n",
|
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" dict(ai=0, aj=1, Ruc=np.array([0, 0, 0])),\n",
|
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" dict(ai=0, aj=2, Ruc=np.array([0, 0, 0])),\n",
|
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" dict(ai=1, aj=2, Ruc=np.array([0, 0, 0])),\n",
|
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" dict(ai=0, aj=2, Ruc=np.array([-1, -1, 0])),\n",
|
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" dict(ai=1, aj=2, Ruc=np.array([-1, -1, 0])),\n",
|
|
" dict(ai=0, aj=2, Ruc=np.array([-1, 0, 0])),\n",
|
|
" dict(ai=1, aj=2, Ruc=np.array([-1, 0, 0])),\n",
|
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" dict(ai=1, aj=2, Ruc=np.array([-2, 0, 0])),\n",
|
|
" dict(ai=1, aj=2, Ruc=np.array([-3, 0, 0])),\n",
|
|
"]\n",
|
|
"\n",
|
|
"# Brilloun zone sampling and Green function contour integral\n",
|
|
"kset = 3\n",
|
|
"kdirs = \"xy\"\n",
|
|
"ebot = -13\n",
|
|
"eset = 300\n",
|
|
"esetp = 1000\n",
|
|
"################################################################################\n",
|
|
"#################################### INPUT #####################################\n",
|
|
"################################################################################"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 5,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"================================================================================================================================================================\n",
|
|
"Input file: \n",
|
|
"/Users/danielpozsar/Downloads/nojij/Fe3GeTe2/monolayer/soc/lat3_791/Fe3GeTe2.fdf\n",
|
|
"Output file: \n",
|
|
"./Fe3GeTe2_notebook.pickle\n",
|
|
"Number of nodes in the parallel cluster: 1\n",
|
|
"================================================================================================================================================================\n",
|
|
"Cell [Ang]: \n",
|
|
"[[ 3.79100000e+00 0.00000000e+00 0.00000000e+00]\n",
|
|
" [-1.89550000e+00 3.28310231e+00 0.00000000e+00]\n",
|
|
" [ 1.25954923e-15 2.18160327e-15 2.05700000e+01]]\n",
|
|
"================================================================================================================================================================\n",
|
|
"DFT axis: \n",
|
|
"[0 0 1]\n",
|
|
"Quantization axis and perpendicular rotation directions:\n",
|
|
"[1 0 0] --» [array([0, 1, 0]), array([0, 0, 1])]\n",
|
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"[0 1 0] --» [array([1, 0, 0]), array([0, 0, 1])]\n",
|
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"[0 0 1] --» [array([1, 0, 0]), array([0, 1, 0])]\n",
|
|
"================================================================================================================================================================\n",
|
|
"Parameters for the contour integral:\n",
|
|
"Number of k points: 3\n",
|
|
"k point directions: xy\n",
|
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"Ebot: -13\n",
|
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"Eset: 300\n",
|
|
"Esetp: 1000\n",
|
|
"================================================================================================================================================================\n"
|
|
]
|
|
},
|
|
{
|
|
"ename": "KeyError",
|
|
"evalue": "'calculate_charge'",
|
|
"output_type": "error",
|
|
"traceback": [
|
|
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
|
"\u001b[0;31mKeyError\u001b[0m Traceback (most recent call last)",
|
|
"Cell \u001b[0;32mIn[5], line 43\u001b[0m\n\u001b[1;32m 40\u001b[0m uc_in_sc_idx \u001b[38;5;241m=\u001b[39m dh\u001b[38;5;241m.\u001b[39mlattice\u001b[38;5;241m.\u001b[39msc_index([\u001b[38;5;241m0\u001b[39m, \u001b[38;5;241m0\u001b[39m, \u001b[38;5;241m0\u001b[39m])\n\u001b[1;32m 42\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m rank \u001b[38;5;241m==\u001b[39m root_node:\n\u001b[0;32m---> 43\u001b[0m \u001b[43mprint_parameters\u001b[49m\u001b[43m(\u001b[49m\u001b[43msimulation_parameters\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 44\u001b[0m times[\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124msetup_time\u001b[39m\u001b[38;5;124m\"\u001b[39m] \u001b[38;5;241m=\u001b[39m timer()\n\u001b[1;32m 45\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mSetup done. Elapsed time: \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mtimes[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124msetup_time\u001b[39m\u001b[38;5;124m'\u001b[39m]\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m s\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n",
|
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"File \u001b[0;32m~/Documents/oktatás/elte/phd/grogu_project/.venv/lib/python3.9/site-packages/grogupy/io.py:132\u001b[0m, in \u001b[0;36mprint_parameters\u001b[0;34m(simulation_parameters)\u001b[0m\n\u001b[1;32m 128\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mEsetp: \u001b[39m\u001b[38;5;124m\"\u001b[39m, simulation_parameters[\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mesetp\u001b[39m\u001b[38;5;124m\"\u001b[39m])\n\u001b[1;32m 129\u001b[0m \u001b[38;5;28mprint\u001b[39m(\n\u001b[1;32m 130\u001b[0m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m================================================================================================================================================================\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m 131\u001b[0m )\n\u001b[0;32m--> 132\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[43msimulation_parameters\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43mcalculate_charge\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m]\u001b[49m:\n\u001b[1;32m 133\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mThe calculated charge of the Hamiltonian in the quantization axes: \u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m 134\u001b[0m \u001b[38;5;28mprint\u001b[39m(simulation_parameters[\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mcharges\u001b[39m\u001b[38;5;124m\"\u001b[39m])\n",
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"\u001b[0;31mKeyError\u001b[0m: 'calculate_charge'"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# MPI parameters\n",
|
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"comm = MPI.COMM_WORLD\n",
|
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"size = comm.Get_size()\n",
|
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"rank = comm.Get_rank()\n",
|
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"root_node = 0\n",
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"\n",
|
|
"# rename outfile\n",
|
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"if not outfile.endswith(\".pickle\"):\n",
|
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" outfile += \".pickle\"\n",
|
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"\n",
|
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"simulation_parameters = dict(\n",
|
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" infile=path,\n",
|
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" outfile=outfile,\n",
|
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" scf_xcf_orientation=scf_xcf_orientation,\n",
|
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" ref_xcf_orientations=ref_xcf_orientations,\n",
|
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" kset=kset,\n",
|
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" kdirs=kdirs,\n",
|
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" ebot=ebot,\n",
|
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" eset=eset,\n",
|
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" esetp=esetp,\n",
|
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" parallel_size=size,\n",
|
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")\n",
|
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"\n",
|
|
"# if ebot is not given put it 0.1 eV under the smallest energy\n",
|
|
"if simulation_parameters[\"ebot\"] is None:\n",
|
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" try:\n",
|
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" eigfile = simulation_parameters[\"infile\"][:-3] + \"EIG\"\n",
|
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" simulation_parameters[\"ebot\"] = read_siesta_emin(eigfile) - 0.1\n",
|
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" except:\n",
|
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" print(\"Could not determine ebot.\")\n",
|
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" print(\"Parameter was not given and .EIG file was not found.\")\n",
|
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"# digestion of the input\n",
|
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"# read sile\n",
|
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"fdf = sisl.get_sile(simulation_parameters[\"infile\"])\n",
|
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"# read in hamiltonian\n",
|
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"dh = fdf.read_hamiltonian()\n",
|
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"simulation_parameters[\"cell\"] = fdf.read_geometry().cell\n",
|
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"\n",
|
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"# unit cell index\n",
|
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"uc_in_sc_idx = dh.lattice.sc_index([0, 0, 0])\n",
|
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"\n",
|
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"if rank == root_node:\n",
|
|
" print_parameters(simulation_parameters)\n",
|
|
" times[\"setup_time\"] = timer()\n",
|
|
" print(f\"Setup done. Elapsed time: {times['setup_time']} s\")\n",
|
|
" print(\n",
|
|
" \"================================================================================================================================================================\"\n",
|
|
" )"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"hh, ss, NO = build_hh_ss(dh)\n",
|
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"\n",
|
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"\n",
|
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"# symmetrizing Hamiltonian and overlap matrix to make them hermitian\n",
|
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"for i in range(dh.lattice.sc_off.shape[0]):\n",
|
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" j = dh.lattice.sc_index(-dh.lattice.sc_off[i])\n",
|
|
" h1, h1d = hh[i], hh[j]\n",
|
|
" hh[i], hh[j] = (h1 + h1d.T.conj()) / 2, (h1d + h1.T.conj()) / 2\n",
|
|
" s1, s1d = ss[i], ss[j]\n",
|
|
" ss[i], ss[j] = (s1 + s1d.T.conj()) / 2, (s1d + s1.T.conj()) / 2\n",
|
|
"\n",
|
|
"\n",
|
|
"# identifying TRS and TRB parts of the Hamiltonian\n",
|
|
"TAUY = np.kron(np.eye(NO), tau_y)\n",
|
|
"hTR = np.array([TAUY @ hh[i].conj() @ TAUY for i in range(dh.lattice.nsc.prod())])\n",
|
|
"hTRS = (hh + hTR) / 2\n",
|
|
"hTRB = (hh - hTR) / 2\n",
|
|
"\n",
|
|
"# extracting the exchange field\n",
|
|
"traced = [spin_tracer(hTRB[i]) for i in range(dh.lattice.nsc.prod())] # equation 77\n",
|
|
"XCF = np.array(\n",
|
|
" [\n",
|
|
" np.array([f[\"x\"] / 2 for f in traced]),\n",
|
|
" np.array([f[\"y\"] / 2 for f in traced]),\n",
|
|
" np.array([f[\"z\"] / 2 for f in traced]),\n",
|
|
" ]\n",
|
|
") # equation 77\n",
|
|
"\n",
|
|
"\n",
|
|
"# Check if exchange field has scalar part\n",
|
|
"max_xcfs = abs(np.array(np.array([f[\"c\"] / 2 for f in traced]))).max()\n",
|
|
"if max_xcfs > 1e-12:\n",
|
|
" warnings.warn(\n",
|
|
" f\"Exchange field has non negligible scalar part. Largest value is {max_xcfs}\"\n",
|
|
" )\n",
|
|
"\n",
|
|
"if rank == root_node:\n",
|
|
" times[\"H_and_XCF_time\"] = timer()\n",
|
|
" print(\n",
|
|
" f\"Hamiltonian and exchange field rotated. Elapsed time: {times['H_and_XCF_time']} s\"\n",
|
|
" )\n",
|
|
" print(\n",
|
|
" \"================================================================================================================================================================\"\n",
|
|
" )"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"pairs, magnetic_entities = setup_pairs_and_magnetic_entities(\n",
|
|
" magnetic_entities, pairs, dh, simulation_parameters\n",
|
|
")\n",
|
|
"\n",
|
|
"if rank == root_node:\n",
|
|
" times[\"site_and_pair_dictionaries_time\"] = timer()\n",
|
|
" print(\n",
|
|
" f\"Site and pair dictionaries created. Elapsed time: {times['site_and_pair_dictionaries_time']} s\"\n",
|
|
" )\n",
|
|
" print(\n",
|
|
" \"================================================================================================================================================================\"\n",
|
|
" )"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"kset = make_kset(\n",
|
|
" dirs=simulation_parameters[\"kdirs\"], NUMK=simulation_parameters[\"kset\"]\n",
|
|
") # generate k space sampling\n",
|
|
"wkset = np.ones(len(kset)) / len(kset) # generate weights for k points\n",
|
|
"kpcs = np.array_split(kset, size) # split the k points based on MPI size\n",
|
|
"\n",
|
|
"if tqdm_imported:\n",
|
|
" kpcs[root_node] = tqdm(kpcs[root_node], desc=\"k loop\")\n",
|
|
"\n",
|
|
"if rank == root_node:\n",
|
|
" times[\"k_set_time\"] = timer()\n",
|
|
" print(f\"k set created. Elapsed time: {times['k_set_time']} s\")\n",
|
|
" print(\n",
|
|
" \"================================================================================================================================================================\"\n",
|
|
" )"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# this will contain the three hamiltonians in the reference directions needed to calculate the energy variations upon rotation\n",
|
|
"hamiltonians = []\n",
|
|
"\n",
|
|
"# iterate over the reference directions (quantization axes)\n",
|
|
"for i, orient in enumerate(simulation_parameters[\"ref_xcf_orientations\"]):\n",
|
|
" # obtain rotated exchange field\n",
|
|
" R = RotMa2b(simulation_parameters[\"scf_xcf_orientation\"], orient[\"o\"])\n",
|
|
" rot_XCF = np.einsum(\"ij,jklm->iklm\", R, XCF)\n",
|
|
" rot_H_XCF = sum(\n",
|
|
" [np.kron(rot_XCF[i], tau) for i, tau in enumerate([tau_x, tau_y, tau_z])]\n",
|
|
" )\n",
|
|
" rot_H_XCF_uc = rot_H_XCF[uc_in_sc_idx]\n",
|
|
"\n",
|
|
" # obtain total Hamiltonian with the rotated exchange field\n",
|
|
" rot_H = hTRS + rot_H_XCF # equation 76\n",
|
|
"\n",
|
|
" hamiltonians.append(\n",
|
|
" dict(\n",
|
|
" orient=orient[\"o\"],\n",
|
|
" H=rot_H,\n",
|
|
" GS=np.zeros(\n",
|
|
" (simulation_parameters[\"eset\"], rot_H.shape[1], rot_H.shape[2]),\n",
|
|
" dtype=\"complex128\",\n",
|
|
" ),\n",
|
|
" GS_tmp=np.zeros(\n",
|
|
" (simulation_parameters[\"eset\"], rot_H.shape[1], rot_H.shape[2]),\n",
|
|
" dtype=\"complex128\",\n",
|
|
" ),\n",
|
|
" )\n",
|
|
" ) # store orientation and rotated Hamiltonian\n",
|
|
"\n",
|
|
" # these are the rotations (for now) perpendicular to the quantization axis\n",
|
|
" for u in orient[\"vw\"]:\n",
|
|
" Tu = np.kron(np.eye(NO, dtype=int), tau_u(u)) # section 2.H\n",
|
|
"\n",
|
|
" Vu1, Vu2 = calc_Vu(rot_H_XCF_uc, Tu)\n",
|
|
"\n",
|
|
" for mag_ent in magnetic_entities:\n",
|
|
" idx = mag_ent[\"spin_box_indeces\"]\n",
|
|
" # fill up the perturbed potentials (for now) based on the on-site projections\n",
|
|
" mag_ent[\"Vu1\"][i].append(Vu1[:, idx][idx, :])\n",
|
|
" mag_ent[\"Vu2\"][i].append(Vu2[:, idx][idx, :])\n",
|
|
"\n",
|
|
"if rank == root_node:\n",
|
|
" times[\"reference_rotations_time\"] = timer()\n",
|
|
" print(\n",
|
|
" f\"Rotations done perpendicular to quantization axis. Elapsed time: {times['reference_rotations_time']} s\"\n",
|
|
" )\n",
|
|
" print(\n",
|
|
" \"================================================================================================================================================================\"\n",
|
|
" )"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"if rank == root_node:\n",
|
|
" print(\"Starting matrix inversions.\")\n",
|
|
" print(f\"Total number of k points: {kset.shape[0]}\")\n",
|
|
" print(f\"Number of energy samples per k point: {simulation_parameters['eset']}\")\n",
|
|
" print(f\"Total number of directions: {len(hamiltonians)}\")\n",
|
|
" print(\n",
|
|
" f\"Total number of matrix inversions: {kset.shape[0] * len(hamiltonians) * simulation_parameters['eset']}\"\n",
|
|
" )\n",
|
|
" print(f\"The shape of the Hamiltonian and the Greens function is {NO}x{NO}={NO*NO}\")\n",
|
|
" # https://stackoverflow.com/questions/70746660/how-to-predict-memory-requirement-for-np-linalg-inv\n",
|
|
" # memory is O(64 n**2) for complex matrices\n",
|
|
" memory_size = getsizeof(hamiltonians[0][\"H\"].base) / 1024\n",
|
|
" print(\n",
|
|
" f\"Memory taken by a single Hamiltonian is: {getsizeof(hamiltonians[0]['H'].base) / 1024} KB\"\n",
|
|
" )\n",
|
|
" print(f\"Expected memory usage per matrix inversion: {memory_size * 32} KB\")\n",
|
|
" print(\n",
|
|
" f\"Expected memory usage per k point for parallel inversion: {memory_size * len(hamiltonians) * simulation_parameters['eset'] * 32} KB\"\n",
|
|
" )\n",
|
|
" print(\n",
|
|
" f\"Expected memory usage on root node: {len(np.array_split(kset, size)[0]) * memory_size * len(hamiltonians) * simulation_parameters['eset'] * 32 / 1024} MB\"\n",
|
|
" )\n",
|
|
" print(\n",
|
|
" \"================================================================================================================================================================\"\n",
|
|
" )\n",
|
|
"\n",
|
|
"comm.Barrier()\n",
|
|
"# ----------------------------------------------------------------------\n",
|
|
"\n",
|
|
"# make energy contour\n",
|
|
"# we are working in eV now !\n",
|
|
"# and sisl shifts E_F to 0 !\n",
|
|
"cont = make_contour(\n",
|
|
" emin=simulation_parameters[\"ebot\"],\n",
|
|
" enum=simulation_parameters[\"eset\"],\n",
|
|
" p=simulation_parameters[\"esetp\"],\n",
|
|
")\n",
|
|
"eran = cont.ze\n",
|
|
"\n",
|
|
"# ----------------------------------------------------------------------\n",
|
|
"# sampling the integrand on the contour and the BZ\n",
|
|
"for k in kpcs[rank]:\n",
|
|
" wk = wkset[rank] # weight of k point in BZ integral\n",
|
|
" # iterate over reference directions\n",
|
|
" for i, hamiltonian_orientation in enumerate(hamiltonians):\n",
|
|
" # calculate Greens function\n",
|
|
" H = hamiltonian_orientation[\"H\"]\n",
|
|
" HK, SK = hsk(H, ss, dh.sc_off, k)\n",
|
|
"\n",
|
|
" # solve Greens function sequentially for the energies, because of memory bound\n",
|
|
" Gk = sequential_GK(HK, SK, eran, simulation_parameters[\"eset\"])\n",
|
|
"\n",
|
|
" # saving this for total charge\n",
|
|
" hamiltonian_orientation[\"GS_tmp\"] += Gk @ SK * wk\n",
|
|
"\n",
|
|
" # store the Greens function slice of the magnetic entities (for now) based on the on-site projections\n",
|
|
" for mag_ent in magnetic_entities:\n",
|
|
" mag_ent[\"Gii_tmp\"][i] += (\n",
|
|
" Gk[:, mag_ent[\"spin_box_indeces\"], :][:, :, mag_ent[\"spin_box_indeces\"]]\n",
|
|
" * wk\n",
|
|
" )\n",
|
|
"\n",
|
|
" for pair in pairs:\n",
|
|
" # add phase shift based on the cell difference\n",
|
|
" phase = np.exp(1j * 2 * np.pi * k @ pair[\"Ruc\"].T)\n",
|
|
"\n",
|
|
" # get the pair orbital sizes from the magnetic entities\n",
|
|
" ai = magnetic_entities[pair[\"ai\"]][\"spin_box_indeces\"]\n",
|
|
" aj = magnetic_entities[pair[\"aj\"]][\"spin_box_indeces\"]\n",
|
|
"\n",
|
|
" # store the Greens function slice of the magnetic entities (for now) based on the on-site projections\n",
|
|
" pair[\"Gij_tmp\"][i] += Gk[:, ai][..., aj] * phase * wk\n",
|
|
" pair[\"Gji_tmp\"][i] += Gk[:, aj][..., ai] / phase * wk\n",
|
|
"\n",
|
|
"# summ reduce partial results of mpi nodes\n",
|
|
"for i in range(len(hamiltonians)):\n",
|
|
" # for total charge\n",
|
|
" comm.Reduce(hamiltonians[i][\"GS_tmp\"], hamiltonians[i][\"GS\"], root=root_node)\n",
|
|
"\n",
|
|
" for mag_ent in magnetic_entities:\n",
|
|
" comm.Reduce(mag_ent[\"Gii_tmp\"][i], mag_ent[\"Gii\"][i], root=root_node)\n",
|
|
"\n",
|
|
" for pair in pairs:\n",
|
|
" comm.Reduce(pair[\"Gij_tmp\"][i], pair[\"Gij\"][i], root=root_node)\n",
|
|
" comm.Reduce(pair[\"Gji_tmp\"][i], pair[\"Gji\"][i], root=root_node)\n",
|
|
"\n",
|
|
"if rank == root_node:\n",
|
|
" times[\"green_function_inversion_time\"] = timer()\n",
|
|
" print(\n",
|
|
" f\"Calculated Greens functions. Elapsed time: {times['green_function_inversion_time']} s\"\n",
|
|
" )\n",
|
|
" print(\n",
|
|
" \"================================================================================================================================================================\"\n",
|
|
" )"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"if rank == root_node:\n",
|
|
" # Calculate total charge\n",
|
|
" for hamiltonian in hamiltonians:\n",
|
|
" GS = hamiltonian[\"GS\"]\n",
|
|
" traced = np.trace((GS), axis1=1, axis2=2)\n",
|
|
" print(\"Total charge: \", int_de_ke(traced, cont.we))\n",
|
|
"\n",
|
|
" # iterate over the magnetic entities\n",
|
|
" for tracker, mag_ent in enumerate(magnetic_entities):\n",
|
|
" # iterate over the quantization axes\n",
|
|
" for i, Gii in enumerate(mag_ent[\"Gii\"]):\n",
|
|
" storage = []\n",
|
|
" # iterate over the first and second order local perturbations\n",
|
|
" for Vu1, Vu2 in zip(mag_ent[\"Vu1\"][i], mag_ent[\"Vu2\"][i]):\n",
|
|
" # The Szunyogh-Lichtenstein formula\n",
|
|
" traced = np.trace((Vu2 @ Gii + 0.5 * Gii @ Vu1 @ Gii), axis1=1, axis2=2)\n",
|
|
" # evaluation of the contour integral\n",
|
|
" storage.append(int_de_ke(traced, cont.we))\n",
|
|
"\n",
|
|
" # fill up the magnetic entities dictionary with the energies\n",
|
|
" magnetic_entities[tracker][\"energies\"].append(storage)\n",
|
|
" # convert to np array\n",
|
|
" magnetic_entities[tracker][\"energies\"] = np.array(\n",
|
|
" magnetic_entities[tracker][\"energies\"]\n",
|
|
" )\n",
|
|
" print(\"Magnetic entities integrated.\")\n",
|
|
"\n",
|
|
" # iterate over the pairs\n",
|
|
" for tracker, pair in enumerate(pairs):\n",
|
|
" # iterate over the quantization axes\n",
|
|
" for i, (Gij, Gji) in enumerate(zip(pair[\"Gij\"], pair[\"Gji\"])):\n",
|
|
" site_i = magnetic_entities[pair[\"ai\"]]\n",
|
|
" site_j = magnetic_entities[pair[\"aj\"]]\n",
|
|
"\n",
|
|
" storage = []\n",
|
|
" # iterate over the first order local perturbations in all possible orientations for the two sites\n",
|
|
" for Vui in site_i[\"Vu1\"][i]:\n",
|
|
" for Vuj in site_j[\"Vu1\"][i]:\n",
|
|
" # The Szunyogh-Lichtenstein formula\n",
|
|
" traced = np.trace((Vui @ Gij @ Vuj @ Gji), axis1=1, axis2=2)\n",
|
|
" # evaluation of the contour integral\n",
|
|
" storage.append(int_de_ke(traced, cont.we))\n",
|
|
" # fill up the pairs dictionary with the energies\n",
|
|
" pairs[tracker][\"energies\"].append(storage)\n",
|
|
" # convert to np array\n",
|
|
" pairs[tracker][\"energies\"] = np.array(pairs[tracker][\"energies\"])\n",
|
|
"\n",
|
|
" print(\"Pairs integrated.\")\n",
|
|
"\n",
|
|
" # calculate magnetic parameters\n",
|
|
" for mag_ent in magnetic_entities:\n",
|
|
" Kxx, Kyy, Kzz, consistency = calculate_anisotropy_tensor(mag_ent)\n",
|
|
" mag_ent[\"K\"] = np.array([Kxx, Kyy, Kzz]) * sisl.unit_convert(\"eV\", \"meV\")\n",
|
|
" mag_ent[\"K_consistency\"] = consistency\n",
|
|
"\n",
|
|
" for pair in pairs:\n",
|
|
" J_iso, J_S, D, J = calculate_exchange_tensor(pair)\n",
|
|
" pair[\"J_iso\"] = J_iso * sisl.unit_convert(\"eV\", \"meV\")\n",
|
|
" pair[\"J_S\"] = J_S * sisl.unit_convert(\"eV\", \"meV\")\n",
|
|
" pair[\"D\"] = D * sisl.unit_convert(\"eV\", \"meV\")\n",
|
|
" pair[\"J\"] = J * sisl.unit_convert(\"eV\", \"meV\")\n",
|
|
"\n",
|
|
" print(\"Magnetic parameters calculated.\")\n",
|
|
"\n",
|
|
" times[\"end_time\"] = timer()\n",
|
|
" print(\n",
|
|
" \"##################################################################### GROGU OUTPUT #############################################################################\"\n",
|
|
" )\n",
|
|
"\n",
|
|
" print_parameters(simulation_parameters)\n",
|
|
" print_atoms_and_pairs(magnetic_entities, pairs)\n",
|
|
" print_runtime_information(times)\n",
|
|
"\n",
|
|
" pairs, magnetic_entities = remove_clutter_for_save(pairs, magnetic_entities)\n",
|
|
" # create output dictionary with all the relevant data\n",
|
|
" results = dict(\n",
|
|
" parameters=simulation_parameters,\n",
|
|
" magnetic_entities=magnetic_entities,\n",
|
|
" pairs=pairs,\n",
|
|
" runtime=times,\n",
|
|
" )\n",
|
|
"\n",
|
|
" save_pickle(simulation_parameters[\"outfile\"], results)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"========================================\n",
|
|
" \n",
|
|
"Atom Angstrom\n",
|
|
"# Label, x y z Sx Sy Sz #Q Lx Ly Lz Jx Jy Jz\n",
|
|
"--------------------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
|
|
"Te1 1.8955 1.0943 13.1698 -0.0000 0.0000 -0.1543 # 5.9345 -0.0000 0.0000 -0.0537 -0.0000 0.0000 -0.2080 \n",
|
|
"Te2 1.8955 1.0943 7.4002 0.0000 -0.0000 -0.1543 # 5.9345 0.0000 -0.0000 -0.0537 0.0000 -0.0000 -0.2080 \n",
|
|
"Ge3 -0.0000 2.1887 10.2850 0.0000 0.0000 -0.1605 # 3.1927 -0.0000 0.0000 0.0012 0.0000 0.0000 -0.1593 \n",
|
|
"Fe4 -0.0000 0.0000 11.6576 0.0001 -0.0001 2.0466 # 8.3044 0.0000 -0.0000 0.1606 0.0001 -0.0001 2.2072 \n",
|
|
"Fe5 -0.0000 0.0000 8.9124 -0.0001 0.0001 2.0466 # 8.3044 -0.0000 0.0000 0.1606 -0.0001 0.0001 2.2072 \n",
|
|
"Fe6 1.8955 1.0944 10.2850 0.0000 0.0000 1.5824 # 8.3296 -0.0000 -0.0000 0.0520 -0.0000 0.0000 1.6344 \n",
|
|
"==================================================================================================================================\n",
|
|
" \n",
|
|
"Exchange meV\n",
|
|
"--------------------------------------------------------------------------------\n",
|
|
"# at1 at2 i j k # d (Ang)\n",
|
|
"--------------------------------------------------------------------------------\n",
|
|
"Fe4 Fe5 0 0 0 # 2.7452\n",
|
|
"Isotropic -82.0854\n",
|
|
"DMI 0.12557 -0.00082199 6.9668e-08\n",
|
|
"Symmetric-anisotropy -0.60237 -0.83842 -0.00032278 -1.2166e-05 -3.3923e-05\n",
|
|
"--------------------------------------------------------------------------------\n",
|
|
"Fe4 Fe6 0 0 0 # 2.5835\n",
|
|
"Isotropic -41.9627\n",
|
|
"DMI 1.1205 -1.9532 0.0018386\n",
|
|
"Symmetric-anisotropy 0.26007 -0.00013243 0.12977 -0.069979 -0.042066\n",
|
|
"--------------------------------------------------------------------------------\n",
|
|
"\n",
|
|
"\n",
|
|
"On-site meV\n",
|
|
"----------------------------------------\n",
|
|
"Fe4\n",
|
|
"0.16339\t0.16068\t0\t0\t0\t0\n",
|
|
"========================================\n"
|
|
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