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b11ab970d6
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import os
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from sys import stdout
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from tqdm import tqdm
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from timeit import default_timer as timer
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os.environ["OMP_NUM_THREADS"] = "1" # export OMP_NUM_THREADS=4
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os.environ["OPENBLAS_NUM_THREADS"] = "1" # export OPENBLAS_NUM_THREADS=4
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os.environ["MKL_NUM_THREADS"] = "1" # export MKL_NUM_THREADS=6
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os.environ["VECLIB_MAXIMUM_THREADS"] = "1" # export VECLIB_MAXIMUM_THREADS=4
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os.environ["NUMEXPR_NUM_THREADS"] = "1" # export NUMEXPR_NUM_THREADS=6
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import numpy as np
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import sisl
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from grogu.useful import *
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from mpi4py import MPI
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from numpy.linalg import inv
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import warnings
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start_time = timer()
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# this cell mimicks an input file
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fdf = sisl.get_sile(
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"/Users/danielpozsar/Downloads/nojij/Fe3GeTe2/monolayer/soc/lat3_791/Fe3GeTe2.fdf"
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)
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# this information needs to be given at the input!!
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scf_xcf_orientation = np.array([0, 0, 1]) # z
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# list of reference directions for around which we calculate the derivatives
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# o is the quantization axis, v and w are two axes perpendicular to it
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# at this moment the user has to supply o,v,w on the input.
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# we can have some default for this
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ref_xcf_orientations = [
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dict(o=np.array([1, 0, 0]), vw=[np.array([0, 1, 0]), np.array([0, 0, 1])]),
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dict(o=np.array([0, 1, 0]), vw=[np.array([1, 0, 0]), np.array([0, 0, 1])]),
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dict(o=np.array([0, 0, 1]), vw=[np.array([1, 0, 0]), np.array([0, 1, 0])]),
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]
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# human readable definition of magnetic entities
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magnetic_entities = [
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dict(atom=3, l=2),
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dict(atom=4, l=2),
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dict(atom=5, l=2),
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# dict(atom=[3, 4]),
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]
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# pair information
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pairs = [
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dict(ai=0, aj=1, Ruc=np.array([0, 0, 0])), # isotropic should be -82 meV
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dict(ai=0, aj=2, Ruc=np.array([0, 0, 0])), # these should all be around -41.9 in the isotropic part
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# dict(ai=1, aj=2, Ruc=np.array([0, 0, 0])),
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# dict(ai=0, aj=2, Ruc=np.array([-1, 0, 0])),
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# dict(ai=1, aj=2, Ruc=np.array([-1, 0, 0])),
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]
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# Brilloun zone sampling and Green function contour integral
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kset = 20
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kdirs = "xy"
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ebot = -30
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eset = 100
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esetp = 10000
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# MPI parameters
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comm = MPI.COMM_WORLD
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size = comm.Get_size()
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rank = comm.Get_rank()
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root_node = 0
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if rank == root_node:
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print("Number of nodes in the parallel cluster: ", size)
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simulation_parameters = dict(path="Not yet specified.",
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scf_xcf_orientation=scf_xcf_orientation,
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ref_xcf_orientations=ref_xcf_orientations,
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kset=kset,
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kdirs=kdirs,
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ebot=ebot,
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eset=eset,
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esetp=esetp,
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parallel_size=size)
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# digestion of the input
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# read in hamiltonian
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dh = fdf.read_hamiltonian()
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try:
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simulation_parameters["geom"] = fdf.read_geometry()
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except:
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print("Error reading geometry.")
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# unit cell index
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uc_in_sc_idx = dh.lattice.sc_index([0, 0, 0])
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setup_time = timer()
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NO = dh.no # shorthand for number of orbitals in the unit cell
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# preprocessing Hamiltonian and overlap matrix elements
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h11 = dh.tocsr(dh.M11r)
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h11 += dh.tocsr(dh.M11i) * 1.0j
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h11 = h11.toarray().reshape(NO, dh.n_s, NO).transpose(0, 2, 1).astype("complex128")
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h22 = dh.tocsr(dh.M22r)
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h22 += dh.tocsr(dh.M22i) * 1.0j
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h22 = h22.toarray().reshape(NO, dh.n_s, NO).transpose(0, 2, 1).astype("complex128")
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h12 = dh.tocsr(dh.M12r)
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h12 += dh.tocsr(dh.M12i) * 1.0j
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h12 = h12.toarray().reshape(NO, dh.n_s, NO).transpose(0, 2, 1).astype("complex128")
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h21 = dh.tocsr(dh.M21r)
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h21 += dh.tocsr(dh.M21i) * 1.0j
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h21 = h21.toarray().reshape(NO, dh.n_s, NO).transpose(0, 2, 1).astype("complex128")
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sov = (
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dh.tocsr(dh.S_idx)
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.toarray()
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.reshape(NO, dh.n_s, NO)
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.transpose(0, 2, 1)
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.astype("complex128")
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)
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# Reorganization of Hamiltonian and overlap matrix elements to SPIN BOX representation
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U = np.vstack(
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[np.kron(np.eye(NO, dtype=int), [1, 0]), np.kron(np.eye(NO, dtype=int), [0, 1])]
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)
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# This is the permutation that transforms ud1ud2 to u12d12
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# That is this transforms FROM SPIN BOX to ORBITAL BOX => U
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# the inverse transformation is U.T u12d12 to ud1ud2
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# That is FROM ORBITAL BOX to SPIN BOX => U.T
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# From now on everything is in SPIN BOX!!
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hh, ss = np.array(
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[
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U.T @ np.block([[h11[:, :, i], h12[:, :, i]], [h21[:, :, i], h22[:, :, i]]]) @ U
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for i in range(dh.lattice.nsc.prod())
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]
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), np.array(
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[
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U.T
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@ np.block([[sov[:, :, i], sov[:, :, i] * 0], [sov[:, :, i] * 0, sov[:, :, i]]])
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@ U
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for i in range(dh.lattice.nsc.prod())
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]
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)
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# symmetrizing Hamiltonian and overlap matrix to make them hermitian
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for i in range(dh.lattice.sc_off.shape[0]):
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j = dh.lattice.sc_index(-dh.lattice.sc_off[i])
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h1, h1d = hh[i], hh[j]
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hh[i], hh[j] = (h1 + h1d.T.conj()) / 2, (h1d + h1.T.conj()) / 2
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s1, s1d = ss[i], ss[j]
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ss[i], ss[j] = (s1 + s1d.T.conj()) / 2, (s1d + s1.T.conj()) / 2
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# identifying TRS and TRB parts of the Hamiltonian
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TAUY = np.kron(np.eye(NO), tau_y)
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hTR = np.array([TAUY @ hh[i].conj() @ TAUY for i in range(dh.lattice.nsc.prod())])
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hTRS = (hh + hTR) / 2
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hTRB = (hh - hTR) / 2
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# extracting the exchange field
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traced = [spin_tracer(hTRB[i]) for i in range(dh.lattice.nsc.prod())] # equation 77
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XCF = np.array(
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[
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np.array([f["x"] for f in traced]),
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np.array([f["y"] for f in traced]),
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np.array([f["z"] for f in traced]),
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]
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) # equation 77
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# Check if exchange field has scalar part
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max_xcfs = abs(np.array(np.array([f["c"] for f in traced]))).max()
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if max_xcfs > 1e-12:
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warnings.warn(
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f"Exchange field has non negligible scalar part. Largest value is {max_xcfs}"
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)
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H_and_XCF_time = timer()
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# for every site we have to store 3 Greens function (and the associated _tmp-s) in the 3 reference directions
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for i, mag_ent in enumerate(magnetic_entities):
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parsed = parse_magnetic_entity(dh, **mag_ent) # parse orbital indexes
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magnetic_entities[i]["orbital_indeces"] = parsed
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magnetic_entities[i]["spin_box_indeces"] = blow_up_orbindx(
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parsed
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) # calculate spin box indexes
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spin_box_shape = len(
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mag_ent["spin_box_indeces"]
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) # calculate size for Greens function generation
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mag_ent["energies"] = [] # we will store the second order energy derivations here
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mag_ent["Gii"] = [] # Greens function
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mag_ent["Gii_tmp"] = [] # Greens function for parallelization
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mag_ent["Vu1"] = [
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list([]) for _ in range(len(ref_xcf_orientations))
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] # These will be the perturbed potentials from eq. 100
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mag_ent["Vu2"] = [list([]) for _ in range(len(ref_xcf_orientations))]
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for i in ref_xcf_orientations:
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mag_ent["Gii"].append(
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np.zeros((eset, spin_box_shape, spin_box_shape), dtype="complex128")
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) # Greens functions for every quantization axis
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mag_ent["Gii_tmp"].append(
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np.zeros((eset, spin_box_shape, spin_box_shape), dtype="complex128")
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)
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# for every site we have to store 2x3 Greens function (and the associated _tmp-s)
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# in the 3 reference directions, because G_ij and G_ji are both needed
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for pair in pairs:
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spin_box_shape_i, spin_box_shape_j = len(
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magnetic_entities[pair["ai"]]["spin_box_indeces"]
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), len(
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magnetic_entities[pair["aj"]]["spin_box_indeces"]
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) # calculate size for Greens function generation
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pair["energies"] = [] # we will store the second order energy derivations here
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pair["Gij"] = [] # Greens function
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pair["Gji"] = []
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pair["Gij_tmp"] = [] # Greens function for parallelization
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pair["Gji_tmp"] = []
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pair["Vij"] = [
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list([]) for _ in range(len(ref_xcf_orientations))
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] # These will be the perturbed potentials from eq. 100
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pair["Vji"] = [list([]) for _ in range(len(ref_xcf_orientations))]
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for i in ref_xcf_orientations:
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pair["Gij"].append(
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np.zeros((eset, spin_box_shape_i, spin_box_shape_j), dtype="complex128")
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)
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pair["Gij_tmp"].append(
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np.zeros((eset, spin_box_shape_i, spin_box_shape_j), dtype="complex128")
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) # Greens functions for every quantization axis
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pair["Gji"].append(
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np.zeros((eset, spin_box_shape_j, spin_box_shape_i), dtype="complex128")
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)
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pair["Gji_tmp"].append(
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np.zeros((eset, spin_box_shape_j, spin_box_shape_i), dtype="complex128")
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)
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site_and_pair_dictionaries_time = timer()
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kset = make_kset(dirs=kdirs, NUMK=kset) # generate k space sampling
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wkset = np.ones(len(kset)) / len(kset) # generate weights for k points
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kpcs = np.array_split(kset, size) # split the k points based on MPI size
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kpcs[root_node] = tqdm(kpcs[root_node], desc='k loop', file=stdout)
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k_set_time = timer()
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# this will contain all the data needed to calculate the energy variations upon rotation
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hamiltonians = []
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# iterate over the reference directions (quantization axes)
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for i, orient in enumerate(ref_xcf_orientations):
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# obtain rotated exchange field
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R = RotMa2b(scf_xcf_orientation, orient["o"])
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rot_XCF = np.einsum("ij,jklm->iklm", R, XCF)
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rot_H_XCF = sum(
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[np.kron(rot_XCF[i], tau) for i, tau in enumerate([tau_x, tau_y, tau_z])]
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)
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rot_H_XCF_uc = rot_H_XCF[uc_in_sc_idx]
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# obtain total Hamiltonian with the rotated exchange field
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rot_H = hTRS + rot_H_XCF # equation 76
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hamiltonians.append(
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dict(orient=orient["o"], H=rot_H, rotations=[])
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) # store orientation and rotated Hamiltonian
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for u in orient[
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"vw"
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]: # these are the infinitezimal rotations (for now) perpendicular to the quantization axis
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Tu = np.kron(np.eye(NO, dtype=int), tau_u(u)) # section 2.H
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Vu1 = 1j / 2 * commutator(rot_H_XCF_uc, Tu) # equation 100
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Vu2 = 1 / 8 * commutator(commutator(Tu, rot_H_XCF_uc), Tu) # equation 100
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for mag_ent in magnetic_entities:
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mag_ent["Vu1"][i].append(
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Vu1[:, mag_ent["spin_box_indeces"]][mag_ent["spin_box_indeces"], :]
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) # fill up the perturbed potentials (for now) based on the on-site projections
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mag_ent["Vu2"][i].append(
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Vu2[:, mag_ent["spin_box_indeces"]][mag_ent["spin_box_indeces"], :]
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)
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for pair in pairs:
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ai = magnetic_entities[pair["ai"]][
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"spin_box_indeces"
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] # get the pair orbital sizes from the magnetic entities
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aj = magnetic_entities[pair["aj"]]["spin_box_indeces"]
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pair["Vij"][i].append(
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Vu1[:, ai][aj, :]
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) # fill up the perturbed potentials (for now) based on the on-site projections
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pair["Vji"][i].append(Vu1[:, aj][ai, :])
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reference_rotations_time = timer()
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if rank == root_node:
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print("Number of magnetic entities being calculated: ", len(magnetic_entities))
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print(
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"We have to calculate the Greens function for three reference direction and we are going to calculate 15 energy integrals per site."
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)
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print(f"The shape of the Hamiltonian and the Greens function is {NO}x{NO}.")
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comm.Barrier()
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# ----------------------------------------------------------------------
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# make energy contour
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# we are working in eV now !
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# and sisil shifts E_F to 0 !
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cont = make_contour(emin=ebot, enum=eset, p=esetp)
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eran = cont.ze
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# ----------------------------------------------------------------------
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# sampling the integrand on the contour and the BZ
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for k in kpcs[rank]:
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wk = wkset[rank] # weight of k point in BZ integral
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for i, hamiltonian_orientation in enumerate(
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hamiltonians
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): # iterate over reference directions
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# calculate Greens function
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H = hamiltonian_orientation["H"]
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HK, SK = hsk(H, ss, dh.sc_off, k)
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Gk = inv(SK * eran.reshape(eset, 1, 1) - HK)
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# store the Greens function slice of the magnetic entities (for now) based on the on-site projections
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for mag_ent in magnetic_entities:
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mag_ent["Gii_tmp"][i] += (
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Gk[:, mag_ent["spin_box_indeces"]][..., mag_ent["spin_box_indeces"]]
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* wk
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)
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for pair in pairs:
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# add phase shift based on the cell difference
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phase = np.exp(1j * 2 * np.pi * k @ pair["Ruc"].T)
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# get the pair orbital sizes from the magnetic entities
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ai = magnetic_entities[pair["ai"]]["spin_box_indeces"]
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aj = magnetic_entities[pair["aj"]]["spin_box_indeces"]
|
||||||
|
|
||||||
|
# store the Greens function slice of the magnetic entities (for now) based on the on-site projections
|
||||||
|
pair["Gij_tmp"][i] += Gk[:, ai][..., aj] * phase * wk
|
||||||
|
pair["Gji_tmp"][i] += Gk[:, aj][..., ai] * phase * wk
|
||||||
|
|
||||||
|
# summ reduce partial results of mpi nodes
|
||||||
|
for i in range(len(hamiltonians)):
|
||||||
|
for mag_ent in magnetic_entities:
|
||||||
|
comm.Reduce(mag_ent["Gii_tmp"][i], mag_ent["Gii"][i], root=root_node)
|
||||||
|
|
||||||
|
for pair in pairs:
|
||||||
|
comm.Reduce(pair["Gij_tmp"][i], pair["Gij"][i], root=root_node)
|
||||||
|
comm.Reduce(pair["Gji_tmp"][i], pair["Gji"][i], root=root_node)
|
||||||
|
|
||||||
|
green_function_inversion_time = timer()
|
||||||
|
|
||||||
|
if rank == root_node:
|
||||||
|
# iterate over the magnetic entities
|
||||||
|
for tracker, mag_ent in enumerate(magnetic_entities):
|
||||||
|
# iterate over the quantization axes
|
||||||
|
for i, Gii in enumerate(mag_ent["Gii"]):
|
||||||
|
storage = []
|
||||||
|
# iterate over the first and second order local perturbations
|
||||||
|
for Vu1, Vu2 in zip(mag_ent["Vu1"][i], mag_ent["Vu2"][i]):
|
||||||
|
# The Szunyogh-Lichtenstein formula
|
||||||
|
traced = np.trace((Vu2 @ Gii + 0.5 * Gii @ Vu1 @ Gii), axis1=1, axis2=2)
|
||||||
|
# evaluation of the contour integral
|
||||||
|
storage.append(np.trapz(-1 / np.pi * np.imag(traced * cont.we)))
|
||||||
|
|
||||||
|
# fill up the magnetic entities dictionary with the energies
|
||||||
|
mag_ent["energies"].append(storage)
|
||||||
|
|
||||||
|
# iterate over the pairs
|
||||||
|
for tracker, pair in enumerate(pairs):
|
||||||
|
# iterate over the quantization axes
|
||||||
|
for i, (Gij, Gji) in enumerate(zip(pair["Gij"], pair["Gji"])):
|
||||||
|
site_i = magnetic_entities[pair["ai"]]
|
||||||
|
site_j = magnetic_entities[pair["aj"]]
|
||||||
|
|
||||||
|
storage = []
|
||||||
|
# iterate over the first order local perturbations in all possible orientations for the two sites
|
||||||
|
for Vui in site_i["Vu1"][i]:
|
||||||
|
for Vuj in site_j["Vu1"][i]:
|
||||||
|
# The Szunyogh-Lichtenstein formula
|
||||||
|
traced = np.trace((Vui @ Gij @ Vuj @ Gji), axis1=1, axis2=2)
|
||||||
|
# evaluation of the contour integral
|
||||||
|
storage.append(np.trapz(-1 / np.pi * np.imag(traced * cont.we)))
|
||||||
|
|
||||||
|
# fill up the pairs dictionary with the energies
|
||||||
|
pairs[tracker]["energies"].append(storage)
|
||||||
|
|
||||||
|
end_time = timer()
|
||||||
|
|
||||||
|
print("############################### GROGU OUTPUT ###################################")
|
||||||
|
print("================================================================================")
|
||||||
|
print("Input file: ")
|
||||||
|
print(simulation_parameters["path"])
|
||||||
|
print("Number of nodes in the parallel cluster: ", simulation_parameters["parallel_size"])
|
||||||
|
print("================================================================================")
|
||||||
|
try:
|
||||||
|
print("Cell [Ang]: ")
|
||||||
|
print(simulation_parameters["geom"].cell)
|
||||||
|
except:
|
||||||
|
print("Geometry could not be read.")
|
||||||
|
print("================================================================================")
|
||||||
|
print("DFT axis: ")
|
||||||
|
print(simulation_parameters["scf_xcf_orientation"])
|
||||||
|
print("Quantization axis and perpendicular rotation directions:")
|
||||||
|
for ref in ref_xcf_orientations:
|
||||||
|
print(ref["o"], " --» ", ref["vw"])
|
||||||
|
print("================================================================================")
|
||||||
|
print("number of k points: ", simulation_parameters["kset"])
|
||||||
|
print("k point directions: ", simulation_parameters["kdirs"])
|
||||||
|
print("================================================================================")
|
||||||
|
print("Parameters for the contour integral:")
|
||||||
|
print("Ebot: ", simulation_parameters["ebot"])
|
||||||
|
print("Eset: ", simulation_parameters["eset"])
|
||||||
|
print("Esetp: ", simulation_parameters["esetp"])
|
||||||
|
print("================================================================================")
|
||||||
|
print("Atomic informations: ")
|
||||||
|
print("")
|
||||||
|
print("")
|
||||||
|
print("Not yet specified.")
|
||||||
|
print("")
|
||||||
|
print("")
|
||||||
|
print("================================================================================")
|
||||||
|
print("Exchange [meV]")
|
||||||
|
print("--------------------------------------------------------------------------------")
|
||||||
|
print("Atom1 Atom2 [i j k] d [Ang]")
|
||||||
|
print("--------------------------------------------------------------------------------")
|
||||||
|
for pair in pairs:
|
||||||
|
J_iso, J_S, D = calculate_exchange_tensor(pair)
|
||||||
|
J_iso = J_iso * sisl.unit_convert("eV", "meV")
|
||||||
|
J_S = J_S * sisl.unit_convert("eV", "meV")
|
||||||
|
D = D * sisl.unit_convert("eV", "meV")
|
||||||
|
|
||||||
|
print(pair["ai"], pair["aj"], pair["Ruc"], "distance")
|
||||||
|
print("Isotropic: ", J_iso)
|
||||||
|
print("DMI: ", D)
|
||||||
|
print("Symmetric-anisotropy: ", J_S)
|
||||||
|
print("")
|
||||||
|
|
||||||
|
print("================================================================================")
|
||||||
|
print("Runtime information: ")
|
||||||
|
print("Total runtime: ", end_time - start_time)
|
||||||
|
print("--------------------------------------------------------------------------------")
|
||||||
|
print("Initial setup: ", setup_time - start_time)
|
||||||
|
print(f"Hamiltonian conversion and XC field extraction: {H_and_XCF_time - setup_time:.3f} s")
|
||||||
|
print(f"Pair and site datastructure creatrions: {site_and_pair_dictionaries_time - H_and_XCF_time:.3f} s")
|
||||||
|
print(f"k set cration and distribution: {k_set_time - site_and_pair_dictionaries_time:.3f} s")
|
||||||
|
print(f"Rotating XC potential: {reference_rotations_time - k_set_time:.3f} s")
|
||||||
|
print(f"Greens function inversion: {green_function_inversion_time - reference_rotations_time:.3f} s")
|
||||||
|
print(f"Calculate energies and magnetic components: {end_time - green_function_inversion_time:.3f} s")
|
||||||
Loading…
Reference in new issue