parent
7403710cf5
commit
cd6e293d23
@ -1,34 +1,71 @@
|
||||
# Relativistic magnetic interactions from non-orthogonal basis sets
|
||||
|
||||
More on the theoretical background can be seen on [arXiv](https://arxiv.org/abs/2309.02558).
|
||||
|
||||
# TODO
|
||||
|
||||
- Definition of magnetic entities:
|
||||
* Through simple sequence o forbitals in the unit cell
|
||||
* Through atom specification
|
||||
* Through atom and orbital specification
|
||||
- Separation of TR and TRB components of the Hamiltonian, Identification of the exchange field.
|
||||
- Definition of commutator expressions, old projection matrix elements
|
||||
- Efficient calculation of Green's functions
|
||||
- Calculation of energy and momentum resolved derivatives
|
||||
- Parallel BZ and serial energy integral
|
||||
- Parallel or serial energy integral to reduce memory overhead
|
||||
- Check the symmetrization of the Hamiltonian and overlap matrix to make them hermitian
|
||||
- Check if exchange field has scalar part
|
||||
- Add more tests
|
||||
- Run tests on different magnetic materials and compare it to Grogu Matlab.
|
||||
- Ehm MAKE IT WORK SOMEHOW :'(
|
||||
|
||||
# Building wheel
|
||||
See detailed documentation on [PYPI](https://packaging.python.org/en/latest/tutorials/packaging-projects/).
|
||||
|
||||
- First you need some API Tokens for Test PYPI ,to be able to upload. You can read about it [here](https://test.pypi.org/help/#apitoken). I own the current project, so you have to contact me.
|
||||
|
||||
|
||||
Use the following commands for a quick setup:
|
||||
|
||||
- Build wheel
|
||||
|
||||
```
|
||||
python -m build
|
||||
```
|
||||
|
||||
- Push to PYPI test repository
|
||||
|
||||
```
|
||||
python -m twine upload --repository testpypi dist/*
|
||||
```
|
||||
|
||||
Build wheel:
|
||||
# Usage
|
||||
|
||||
Push to pypi(testpypi for beginners): python3 -m twine upload --repository testpypi dist/*
|
||||
## For end users
|
||||
Download and install from [PYPI](https://test.pypi.org/project/grogu-magn/) test repository.
|
||||
|
||||
Ehhez kellenek tokenek:
|
||||
You will be prompted for a username and password. For the username, use __token__. For the password, use the token value, including the pypi- prefix.
|
||||
```
|
||||
python3 -m pip install --index-url https://test.pypi.org/simple/ grogu_magn
|
||||
```
|
||||
|
||||
## For developers
|
||||
|
||||
Végfelhasználóknak (egyelőre testpypi): python3 -m pip install --index-url https://test.pypi.org/simple/ example-package-YOUR-USERNAME-HERE
|
||||
- Clone repository from Gitea
|
||||
|
||||
```
|
||||
git clone https://gitea.vo.elte.hu/et209d/grogu.git
|
||||
```
|
||||
|
||||
- Create .venv (for example with VsCode)
|
||||
* Use python 3.9.6
|
||||
* install dependencies from:
|
||||
* requirements.txt
|
||||
* requirements-dev.txt
|
||||
* /docs/requirements.txt
|
||||
|
||||
- Install and run pre-commit
|
||||
|
||||
```
|
||||
pre-commit install
|
||||
pre-commit run --all-files
|
||||
```
|
||||
|
||||
To build the documentation navigate to the `docs/source` folder and run `make clean` and `make html`. After this the html page can be found in `docs/source/_build/html`.
|
||||
|
||||
```
|
||||
cd docs/source
|
||||
make clean
|
||||
make html
|
||||
```
|
||||
|
||||
Binary file not shown.
Binary file not shown.
Binary file not shown.
Binary file not shown.
@ -1,4 +1,4 @@
|
||||
# Sphinx build info version 1
|
||||
# This file records the configuration used when building these files. When it is not found, a full rebuild will be done.
|
||||
config: 0f8ff1598a5b65221fc2ef8f29fdbeac
|
||||
# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
|
||||
config: d8f86c3651bae6bbb2cfa348920c9196
|
||||
tags: 645f666f9bcd5a90fca523b33c5a78b7
|
||||
|
||||
File diff suppressed because one or more lines are too long
@ -0,0 +1,526 @@
|
||||
from useful import *
|
||||
|
||||
|
||||
def main():
|
||||
import os
|
||||
from sys import stdout
|
||||
from timeit import default_timer as timer
|
||||
|
||||
from tqdm import tqdm
|
||||
|
||||
os.environ["OMP_NUM_THREADS"] = "1" # export OMP_NUM_THREADS=4
|
||||
os.environ["OPENBLAS_NUM_THREADS"] = "1" # export OPENBLAS_NUM_THREADS=4
|
||||
os.environ["MKL_NUM_THREADS"] = "1" # export MKL_NUM_THREADS=6
|
||||
os.environ["VECLIB_MAXIMUM_THREADS"] = "1" # export VECLIB_MAXIMUM_THREADS=4
|
||||
os.environ["NUMEXPR_NUM_THREADS"] = "1" # export NUMEXPR_NUM_THREADS=6
|
||||
|
||||
import warnings
|
||||
|
||||
import numpy as np
|
||||
import sisl
|
||||
from mpi4py import MPI
|
||||
from numpy.linalg import inv
|
||||
|
||||
start_time = timer()
|
||||
|
||||
# this cell mimicks an input file
|
||||
fdf = sisl.get_sile("../../lat3_791/Fe3GeTe2.fdf")
|
||||
# this information needs to be given at the input!!
|
||||
scf_xcf_orientation = np.array([0, 0, 1]) # z
|
||||
# list of reference directions for around which we calculate the derivatives
|
||||
# o is the quantization axis, v and w are two axes perpendicular to it
|
||||
# at this moment the user has to supply o,v,w on the input.
|
||||
# we can have some default for this
|
||||
ref_xcf_orientations = [
|
||||
dict(o=np.array([1, 0, 0]), vw=[np.array([0, 1, 0]), np.array([0, 0, 1])]),
|
||||
dict(o=np.array([0, 1, 0]), vw=[np.array([1, 0, 0]), np.array([0, 0, 1])]),
|
||||
dict(o=np.array([0, 0, 1]), vw=[np.array([1, 0, 0]), np.array([0, 1, 0])]),
|
||||
]
|
||||
|
||||
# human readable definition of magnetic entities
|
||||
# magnetic_entities = [
|
||||
# dict(atom=0, ),
|
||||
# dict(atom=1, ),
|
||||
# dict(atom=2, ),
|
||||
# dict(atom=3, l=2),
|
||||
# dict(atom=4, l=2),
|
||||
# dict(atom=5, l=2),
|
||||
# ]
|
||||
# pairs = [
|
||||
# dict(ai=3, aj=4, Ruc=np.array([0, 0, 0])), # isotropic should be -82 meV
|
||||
# dict(ai=3, aj=5, Ruc=np.array([0, 0, 0])), # these should all be around -41.9 in the isotropic part
|
||||
# dict(ai=4, aj=5, Ruc=np.array([0, 0, 0])),
|
||||
# dict(ai=3, aj=0, Ruc=np.array([0, 0, 0])),
|
||||
# dict(ai=3, aj=1, Ruc=np.array([0, 0, 0])),
|
||||
# dict(ai=3, aj=2, Ruc=np.array([0, 0, 0])),
|
||||
# ]
|
||||
magnetic_entities = [
|
||||
dict(atom=3, l=2),
|
||||
dict(atom=4, l=2),
|
||||
dict(atom=5, l=2),
|
||||
]
|
||||
|
||||
# pair information
|
||||
pairs = [
|
||||
dict(ai=0, aj=1, Ruc=np.array([0, 0, 0])), # isotropic should be -82 meV
|
||||
dict(
|
||||
ai=0, aj=2, Ruc=np.array([0, 0, 0])
|
||||
), # these should all be around -41.9 in the isotropic part
|
||||
dict(ai=1, aj=2, Ruc=np.array([0, 0, 0])),
|
||||
dict(ai=0, aj=1, Ruc=np.array([-1, 0, 0])),
|
||||
dict(ai=0, aj=2, Ruc=np.array([-1, 0, 0])),
|
||||
dict(ai=0, aj=1, Ruc=np.array([1, 0, 0])),
|
||||
dict(ai=0, aj=2, Ruc=np.array([1, 0, 0])),
|
||||
dict(ai=0, aj=1, Ruc=np.array([0, -1, 0])),
|
||||
dict(ai=0, aj=2, Ruc=np.array([0, -1, 0])),
|
||||
dict(ai=0, aj=1, Ruc=np.array([0, 1, 0])),
|
||||
dict(ai=0, aj=2, Ruc=np.array([0, 1, 0])),
|
||||
dict(ai=1, aj=2, Ruc=np.array([-1, 0, 0])),
|
||||
]
|
||||
|
||||
# Brilloun zone sampling and Green function contour integral
|
||||
kset = 20
|
||||
kdirs = "xy"
|
||||
ebot = -30
|
||||
eset = 50
|
||||
esetp = 1000
|
||||
|
||||
# MPI parameters
|
||||
comm = MPI.COMM_WORLD
|
||||
size = comm.Get_size()
|
||||
rank = comm.Get_rank()
|
||||
root_node = 0
|
||||
if rank == root_node:
|
||||
print("Number of nodes in the parallel cluster: ", size)
|
||||
|
||||
simulation_parameters = dict(
|
||||
path="Not yet specified.",
|
||||
scf_xcf_orientation=scf_xcf_orientation,
|
||||
ref_xcf_orientations=ref_xcf_orientations,
|
||||
kset=kset,
|
||||
kdirs=kdirs,
|
||||
ebot=ebot,
|
||||
eset=eset,
|
||||
esetp=esetp,
|
||||
parallel_size=size,
|
||||
)
|
||||
|
||||
# digestion of the input
|
||||
# read in hamiltonian
|
||||
dh = fdf.read_hamiltonian()
|
||||
try:
|
||||
simulation_parameters["geom"] = fdf.read_geometry()
|
||||
except:
|
||||
print("Error reading geometry.")
|
||||
|
||||
# unit cell index
|
||||
uc_in_sc_idx = dh.lattice.sc_index([0, 0, 0])
|
||||
|
||||
setup_time = timer()
|
||||
|
||||
NO = dh.no # shorthand for number of orbitals in the unit cell
|
||||
|
||||
# preprocessing Hamiltonian and overlap matrix elements
|
||||
h11 = dh.tocsr(dh.M11r)
|
||||
h11 += dh.tocsr(dh.M11i) * 1.0j
|
||||
h11 = h11.toarray().reshape(NO, dh.n_s, NO).transpose(0, 2, 1).astype("complex128")
|
||||
|
||||
h22 = dh.tocsr(dh.M22r)
|
||||
h22 += dh.tocsr(dh.M22i) * 1.0j
|
||||
h22 = h22.toarray().reshape(NO, dh.n_s, NO).transpose(0, 2, 1).astype("complex128")
|
||||
|
||||
h12 = dh.tocsr(dh.M12r)
|
||||
h12 += dh.tocsr(dh.M12i) * 1.0j
|
||||
h12 = h12.toarray().reshape(NO, dh.n_s, NO).transpose(0, 2, 1).astype("complex128")
|
||||
|
||||
h21 = dh.tocsr(dh.M21r)
|
||||
h21 += dh.tocsr(dh.M21i) * 1.0j
|
||||
h21 = h21.toarray().reshape(NO, dh.n_s, NO).transpose(0, 2, 1).astype("complex128")
|
||||
|
||||
sov = (
|
||||
dh.tocsr(dh.S_idx)
|
||||
.toarray()
|
||||
.reshape(NO, dh.n_s, NO)
|
||||
.transpose(0, 2, 1)
|
||||
.astype("complex128")
|
||||
)
|
||||
|
||||
# Reorganization of Hamiltonian and overlap matrix elements to SPIN BOX representation
|
||||
U = np.vstack(
|
||||
[np.kron(np.eye(NO, dtype=int), [1, 0]), np.kron(np.eye(NO, dtype=int), [0, 1])]
|
||||
)
|
||||
# This is the permutation that transforms ud1ud2 to u12d12
|
||||
# That is this transforms FROM SPIN BOX to ORBITAL BOX => U
|
||||
# the inverse transformation is U.T u12d12 to ud1ud2
|
||||
# That is FROM ORBITAL BOX to SPIN BOX => U.T
|
||||
|
||||
# From now on everything is in SPIN BOX!!
|
||||
hh, ss = np.array(
|
||||
[
|
||||
U.T
|
||||
@ np.block([[h11[:, :, i], h12[:, :, i]], [h21[:, :, i], h22[:, :, i]]])
|
||||
@ U
|
||||
for i in range(dh.lattice.nsc.prod())
|
||||
]
|
||||
), np.array(
|
||||
[
|
||||
U.T
|
||||
@ np.block(
|
||||
[[sov[:, :, i], sov[:, :, i] * 0], [sov[:, :, i] * 0, sov[:, :, i]]]
|
||||
)
|
||||
@ U
|
||||
for i in range(dh.lattice.nsc.prod())
|
||||
]
|
||||
)
|
||||
|
||||
# symmetrizing Hamiltonian and overlap matrix to make them hermitian
|
||||
for i in range(dh.lattice.sc_off.shape[0]):
|
||||
j = dh.lattice.sc_index(-dh.lattice.sc_off[i])
|
||||
h1, h1d = hh[i], hh[j]
|
||||
hh[i], hh[j] = (h1 + h1d.T.conj()) / 2, (h1d + h1.T.conj()) / 2
|
||||
s1, s1d = ss[i], ss[j]
|
||||
ss[i], ss[j] = (s1 + s1d.T.conj()) / 2, (s1d + s1.T.conj()) / 2
|
||||
|
||||
# identifying TRS and TRB parts of the Hamiltonian
|
||||
TAUY = np.kron(np.eye(NO), tau_y)
|
||||
hTR = np.array([TAUY @ hh[i].conj() @ TAUY for i in range(dh.lattice.nsc.prod())])
|
||||
hTRS = (hh + hTR) / 2
|
||||
hTRB = (hh - hTR) / 2
|
||||
|
||||
# extracting the exchange field
|
||||
traced = [spin_tracer(hTRB[i]) for i in range(dh.lattice.nsc.prod())] # equation 77
|
||||
XCF = np.array(
|
||||
[
|
||||
np.array([f["x"] for f in traced]),
|
||||
np.array([f["y"] for f in traced]),
|
||||
np.array([f["z"] for f in traced]),
|
||||
]
|
||||
) # equation 77
|
||||
|
||||
# Check if exchange field has scalar part
|
||||
max_xcfs = abs(np.array(np.array([f["c"] for f in traced]))).max()
|
||||
if max_xcfs > 1e-12:
|
||||
warnings.warn(
|
||||
f"Exchange field has non negligible scalar part. Largest value is {max_xcfs}"
|
||||
)
|
||||
|
||||
H_and_XCF_time = timer()
|
||||
|
||||
# for every site we have to store 3 Greens function (and the associated _tmp-s) in the 3 reference directions
|
||||
for i, mag_ent in enumerate(magnetic_entities):
|
||||
parsed = parse_magnetic_entity(dh, **mag_ent) # parse orbital indexes
|
||||
magnetic_entities[i]["orbital_indeces"] = parsed
|
||||
magnetic_entities[i]["spin_box_indeces"] = blow_up_orbindx(
|
||||
parsed
|
||||
) # calculate spin box indexes
|
||||
spin_box_shape = len(
|
||||
mag_ent["spin_box_indeces"]
|
||||
) # calculate size for Greens function generation
|
||||
|
||||
mag_ent["energies"] = (
|
||||
[]
|
||||
) # we will store the second order energy derivations here
|
||||
|
||||
mag_ent["Gii"] = [] # Greens function
|
||||
mag_ent["Gii_tmp"] = [] # Greens function for parallelization
|
||||
mag_ent["Vu1"] = [
|
||||
list([]) for _ in range(len(ref_xcf_orientations))
|
||||
] # These will be the perturbed potentials from eq. 100
|
||||
mag_ent["Vu2"] = [list([]) for _ in range(len(ref_xcf_orientations))]
|
||||
for i in ref_xcf_orientations:
|
||||
mag_ent["Gii"].append(
|
||||
np.zeros((eset, spin_box_shape, spin_box_shape), dtype="complex128")
|
||||
) # Greens functions for every quantization axis
|
||||
mag_ent["Gii_tmp"].append(
|
||||
np.zeros((eset, spin_box_shape, spin_box_shape), dtype="complex128")
|
||||
)
|
||||
|
||||
# for every site we have to store 2x3 Greens function (and the associated _tmp-s)
|
||||
# in the 3 reference directions, because G_ij and G_ji are both needed
|
||||
for pair in pairs:
|
||||
spin_box_shape_i, spin_box_shape_j = len(
|
||||
magnetic_entities[pair["ai"]]["spin_box_indeces"]
|
||||
), len(
|
||||
magnetic_entities[pair["aj"]]["spin_box_indeces"]
|
||||
) # calculate size for Greens function generation
|
||||
|
||||
pair["energies"] = [] # we will store the second order energy derivations here
|
||||
|
||||
pair["Gij"] = [] # Greens function
|
||||
pair["Gji"] = []
|
||||
pair["Gij_tmp"] = [] # Greens function for parallelization
|
||||
pair["Gji_tmp"] = []
|
||||
|
||||
pair["Vij"] = [
|
||||
list([]) for _ in range(len(ref_xcf_orientations))
|
||||
] # These will be the perturbed potentials from eq. 100
|
||||
pair["Vji"] = [list([]) for _ in range(len(ref_xcf_orientations))]
|
||||
|
||||
for i in ref_xcf_orientations:
|
||||
pair["Gij"].append(
|
||||
np.zeros((eset, spin_box_shape_i, spin_box_shape_j), dtype="complex128")
|
||||
)
|
||||
pair["Gij_tmp"].append(
|
||||
np.zeros((eset, spin_box_shape_i, spin_box_shape_j), dtype="complex128")
|
||||
) # Greens functions for every quantization axis
|
||||
pair["Gji"].append(
|
||||
np.zeros((eset, spin_box_shape_j, spin_box_shape_i), dtype="complex128")
|
||||
)
|
||||
pair["Gji_tmp"].append(
|
||||
np.zeros((eset, spin_box_shape_j, spin_box_shape_i), dtype="complex128")
|
||||
)
|
||||
|
||||
site_and_pair_dictionaries_time = timer()
|
||||
|
||||
kset = make_kset(dirs=kdirs, NUMK=kset) # generate k space sampling
|
||||
wkset = np.ones(len(kset)) / len(kset) # generate weights for k points
|
||||
kpcs = np.array_split(kset, size) # split the k points based on MPI size
|
||||
kpcs[root_node] = tqdm(kpcs[root_node], desc="k loop", file=stdout)
|
||||
|
||||
k_set_time = timer()
|
||||
|
||||
# this will contain all the data needed to calculate the energy variations upon rotation
|
||||
hamiltonians = []
|
||||
|
||||
# iterate over the reference directions (quantization axes)
|
||||
for i, orient in enumerate(ref_xcf_orientations):
|
||||
# obtain rotated exchange field
|
||||
R = RotMa2b(scf_xcf_orientation, orient["o"])
|
||||
rot_XCF = np.einsum("ij,jklm->iklm", R, XCF)
|
||||
rot_H_XCF = sum(
|
||||
[np.kron(rot_XCF[i], tau) for i, tau in enumerate([tau_x, tau_y, tau_z])]
|
||||
)
|
||||
rot_H_XCF_uc = rot_H_XCF[uc_in_sc_idx]
|
||||
|
||||
# obtain total Hamiltonian with the rotated exchange field
|
||||
rot_H = hTRS + rot_H_XCF # equation 76
|
||||
|
||||
hamiltonians.append(
|
||||
dict(orient=orient["o"], H=rot_H, rotations=[])
|
||||
) # store orientation and rotated Hamiltonian
|
||||
|
||||
for u in orient[
|
||||
"vw"
|
||||
]: # these are the infinitezimal rotations (for now) perpendicular to the quantization axis
|
||||
Tu = np.kron(np.eye(NO, dtype=int), tau_u(u)) # section 2.H
|
||||
|
||||
Vu1 = 1j / 2 * commutator(rot_H_XCF_uc, Tu) # equation 100
|
||||
Vu2 = 1 / 8 * commutator(commutator(Tu, rot_H_XCF_uc), Tu) # equation 100
|
||||
|
||||
for mag_ent in magnetic_entities:
|
||||
mag_ent["Vu1"][i].append(
|
||||
Vu1[:, mag_ent["spin_box_indeces"]][mag_ent["spin_box_indeces"], :]
|
||||
) # fill up the perturbed potentials (for now) based on the on-site projections
|
||||
mag_ent["Vu2"][i].append(
|
||||
Vu2[:, mag_ent["spin_box_indeces"]][mag_ent["spin_box_indeces"], :]
|
||||
)
|
||||
|
||||
for pair in pairs:
|
||||
ai = magnetic_entities[pair["ai"]][
|
||||
"spin_box_indeces"
|
||||
] # get the pair orbital sizes from the magnetic entities
|
||||
aj = magnetic_entities[pair["aj"]]["spin_box_indeces"]
|
||||
pair["Vij"][i].append(
|
||||
Vu1[:, ai][aj, :]
|
||||
) # fill up the perturbed potentials (for now) based on the on-site projections
|
||||
pair["Vji"][i].append(Vu1[:, aj][ai, :])
|
||||
|
||||
reference_rotations_time = timer()
|
||||
|
||||
if rank == root_node:
|
||||
print("Number of magnetic entities being calculated: ", len(magnetic_entities))
|
||||
print(
|
||||
"We have to calculate the Greens function for three reference direction and we are going to calculate 15 energy integrals per site."
|
||||
)
|
||||
print(f"The shape of the Hamiltonian and the Greens function is {NO}x{NO}.")
|
||||
comm.Barrier()
|
||||
# ----------------------------------------------------------------------
|
||||
|
||||
# make energy contour
|
||||
# we are working in eV now !
|
||||
# and sisil shifts E_F to 0 !
|
||||
cont = make_contour(emin=ebot, enum=eset, p=esetp)
|
||||
eran = cont.ze
|
||||
|
||||
# ----------------------------------------------------------------------
|
||||
# sampling the integrand on the contour and the BZ
|
||||
for k in kpcs[rank]:
|
||||
wk = wkset[rank] # weight of k point in BZ integral
|
||||
for i, hamiltonian_orientation in enumerate(
|
||||
hamiltonians
|
||||
): # iterate over reference directions
|
||||
# calculate Greens function
|
||||
H = hamiltonian_orientation["H"]
|
||||
HK, SK = hsk(H, ss, dh.sc_off, k)
|
||||
Gk = inv(SK * eran.reshape(eset, 1, 1) - HK)
|
||||
|
||||
# store the Greens function slice of the magnetic entities (for now) based on the on-site projections
|
||||
for mag_ent in magnetic_entities:
|
||||
mag_ent["Gii_tmp"][i] += (
|
||||
Gk[:, mag_ent["spin_box_indeces"]][..., mag_ent["spin_box_indeces"]]
|
||||
* wk
|
||||
)
|
||||
|
||||
for pair in pairs:
|
||||
# add phase shift based on the cell difference
|
||||
phase = np.exp(1j * 2 * np.pi * k @ pair["Ruc"].T)
|
||||
|
||||
# get the pair orbital sizes from the magnetic entities
|
||||
ai = magnetic_entities[pair["ai"]]["spin_box_indeces"]
|
||||
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(print_atomic_indices(pair, magnetic_entities, dh))
|
||||
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"
|
||||
)
|
||||
|
||||
|
||||
if __name__ == "__main__":
|
||||
main()
|
||||
File diff suppressed because one or more lines are too long
@ -1,515 +0,0 @@
|
||||
import os
|
||||
from sys import stdout
|
||||
from timeit import default_timer as timer
|
||||
|
||||
from tqdm import tqdm
|
||||
|
||||
os.environ["OMP_NUM_THREADS"] = "1" # export OMP_NUM_THREADS=4
|
||||
os.environ["OPENBLAS_NUM_THREADS"] = "1" # export OPENBLAS_NUM_THREADS=4
|
||||
os.environ["MKL_NUM_THREADS"] = "1" # export MKL_NUM_THREADS=6
|
||||
os.environ["VECLIB_MAXIMUM_THREADS"] = "1" # export VECLIB_MAXIMUM_THREADS=4
|
||||
os.environ["NUMEXPR_NUM_THREADS"] = "1" # export NUMEXPR_NUM_THREADS=6
|
||||
|
||||
import warnings
|
||||
|
||||
import numpy as np
|
||||
import sisl
|
||||
from mpi4py import MPI
|
||||
from numpy.linalg import inv
|
||||
|
||||
from grogu.useful import *
|
||||
|
||||
start_time = timer()
|
||||
|
||||
# this cell mimicks an input file
|
||||
fdf = sisl.get_sile("./lat3_791/Fe3GeTe2.fdf")
|
||||
# this information needs to be given at the input!!
|
||||
scf_xcf_orientation = np.array([0, 0, 1]) # z
|
||||
# list of reference directions for around which we calculate the derivatives
|
||||
# o is the quantization axis, v and w are two axes perpendicular to it
|
||||
# at this moment the user has to supply o,v,w on the input.
|
||||
# we can have some default for this
|
||||
ref_xcf_orientations = [
|
||||
dict(o=np.array([1, 0, 0]), vw=[np.array([0, 1, 0]), np.array([0, 0, 1])]),
|
||||
dict(o=np.array([0, 1, 0]), vw=[np.array([1, 0, 0]), np.array([0, 0, 1])]),
|
||||
dict(o=np.array([0, 0, 1]), vw=[np.array([1, 0, 0]), np.array([0, 1, 0])]),
|
||||
]
|
||||
|
||||
# human readable definition of magnetic entities
|
||||
# magnetic_entities = [
|
||||
# dict(atom=0, ),
|
||||
# dict(atom=1, ),
|
||||
# dict(atom=2, ),
|
||||
# dict(atom=3, l=2),
|
||||
# dict(atom=4, l=2),
|
||||
# dict(atom=5, l=2),
|
||||
# ]
|
||||
# pairs = [
|
||||
# dict(ai=3, aj=4, Ruc=np.array([0, 0, 0])), # isotropic should be -82 meV
|
||||
# dict(ai=3, aj=5, Ruc=np.array([0, 0, 0])), # these should all be around -41.9 in the isotropic part
|
||||
# dict(ai=4, aj=5, Ruc=np.array([0, 0, 0])),
|
||||
# dict(ai=3, aj=0, Ruc=np.array([0, 0, 0])),
|
||||
# dict(ai=3, aj=1, Ruc=np.array([0, 0, 0])),
|
||||
# dict(ai=3, aj=2, Ruc=np.array([0, 0, 0])),
|
||||
# ]
|
||||
magnetic_entities = [
|
||||
dict(atom=3, l=2),
|
||||
dict(atom=4, l=2),
|
||||
dict(atom=5, l=2),
|
||||
]
|
||||
|
||||
# pair information
|
||||
pairs = [
|
||||
dict(ai=0, aj=1, Ruc=np.array([0, 0, 0])), # isotropic should be -82 meV
|
||||
dict(
|
||||
ai=0, aj=2, Ruc=np.array([0, 0, 0])
|
||||
), # these should all be around -41.9 in the isotropic part
|
||||
dict(ai=1, aj=2, Ruc=np.array([0, 0, 0])),
|
||||
dict(ai=0, aj=1, Ruc=np.array([-1, 0, 0])),
|
||||
dict(ai=0, aj=2, Ruc=np.array([-1, 0, 0])),
|
||||
dict(ai=0, aj=1, Ruc=np.array([1, 0, 0])),
|
||||
dict(ai=0, aj=2, Ruc=np.array([1, 0, 0])),
|
||||
dict(ai=0, aj=1, Ruc=np.array([0, -1, 0])),
|
||||
dict(ai=0, aj=2, Ruc=np.array([0, -1, 0])),
|
||||
dict(ai=0, aj=1, Ruc=np.array([0, 1, 0])),
|
||||
dict(ai=0, aj=2, Ruc=np.array([0, 1, 0])),
|
||||
dict(ai=1, aj=2, Ruc=np.array([-1, 0, 0])),
|
||||
]
|
||||
|
||||
# Brilloun zone sampling and Green function contour integral
|
||||
kset = 20
|
||||
kdirs = "xy"
|
||||
ebot = -30
|
||||
eset = 50
|
||||
esetp = 1000
|
||||
|
||||
|
||||
# MPI parameters
|
||||
comm = MPI.COMM_WORLD
|
||||
size = comm.Get_size()
|
||||
rank = comm.Get_rank()
|
||||
root_node = 0
|
||||
if rank == root_node:
|
||||
print("Number of nodes in the parallel cluster: ", size)
|
||||
|
||||
simulation_parameters = dict(
|
||||
path="Not yet specified.",
|
||||
scf_xcf_orientation=scf_xcf_orientation,
|
||||
ref_xcf_orientations=ref_xcf_orientations,
|
||||
kset=kset,
|
||||
kdirs=kdirs,
|
||||
ebot=ebot,
|
||||
eset=eset,
|
||||
esetp=esetp,
|
||||
parallel_size=size,
|
||||
)
|
||||
|
||||
# digestion of the input
|
||||
# read in hamiltonian
|
||||
dh = fdf.read_hamiltonian()
|
||||
try:
|
||||
simulation_parameters["geom"] = fdf.read_geometry()
|
||||
except:
|
||||
print("Error reading geometry.")
|
||||
|
||||
# unit cell index
|
||||
uc_in_sc_idx = dh.lattice.sc_index([0, 0, 0])
|
||||
|
||||
setup_time = timer()
|
||||
|
||||
NO = dh.no # shorthand for number of orbitals in the unit cell
|
||||
|
||||
# preprocessing Hamiltonian and overlap matrix elements
|
||||
h11 = dh.tocsr(dh.M11r)
|
||||
h11 += dh.tocsr(dh.M11i) * 1.0j
|
||||
h11 = h11.toarray().reshape(NO, dh.n_s, NO).transpose(0, 2, 1).astype("complex128")
|
||||
|
||||
h22 = dh.tocsr(dh.M22r)
|
||||
h22 += dh.tocsr(dh.M22i) * 1.0j
|
||||
h22 = h22.toarray().reshape(NO, dh.n_s, NO).transpose(0, 2, 1).astype("complex128")
|
||||
|
||||
h12 = dh.tocsr(dh.M12r)
|
||||
h12 += dh.tocsr(dh.M12i) * 1.0j
|
||||
h12 = h12.toarray().reshape(NO, dh.n_s, NO).transpose(0, 2, 1).astype("complex128")
|
||||
|
||||
h21 = dh.tocsr(dh.M21r)
|
||||
h21 += dh.tocsr(dh.M21i) * 1.0j
|
||||
h21 = h21.toarray().reshape(NO, dh.n_s, NO).transpose(0, 2, 1).astype("complex128")
|
||||
|
||||
sov = (
|
||||
dh.tocsr(dh.S_idx)
|
||||
.toarray()
|
||||
.reshape(NO, dh.n_s, NO)
|
||||
.transpose(0, 2, 1)
|
||||
.astype("complex128")
|
||||
)
|
||||
|
||||
|
||||
# Reorganization of Hamiltonian and overlap matrix elements to SPIN BOX representation
|
||||
U = np.vstack(
|
||||
[np.kron(np.eye(NO, dtype=int), [1, 0]), np.kron(np.eye(NO, dtype=int), [0, 1])]
|
||||
)
|
||||
# This is the permutation that transforms ud1ud2 to u12d12
|
||||
# That is this transforms FROM SPIN BOX to ORBITAL BOX => U
|
||||
# the inverse transformation is U.T u12d12 to ud1ud2
|
||||
# That is FROM ORBITAL BOX to SPIN BOX => U.T
|
||||
|
||||
# From now on everything is in SPIN BOX!!
|
||||
hh, ss = np.array(
|
||||
[
|
||||
U.T @ np.block([[h11[:, :, i], h12[:, :, i]], [h21[:, :, i], h22[:, :, i]]]) @ U
|
||||
for i in range(dh.lattice.nsc.prod())
|
||||
]
|
||||
), np.array(
|
||||
[
|
||||
U.T
|
||||
@ np.block([[sov[:, :, i], sov[:, :, i] * 0], [sov[:, :, i] * 0, sov[:, :, i]]])
|
||||
@ U
|
||||
for i in range(dh.lattice.nsc.prod())
|
||||
]
|
||||
)
|
||||
|
||||
|
||||
# symmetrizing Hamiltonian and overlap matrix to make them hermitian
|
||||
for i in range(dh.lattice.sc_off.shape[0]):
|
||||
j = dh.lattice.sc_index(-dh.lattice.sc_off[i])
|
||||
h1, h1d = hh[i], hh[j]
|
||||
hh[i], hh[j] = (h1 + h1d.T.conj()) / 2, (h1d + h1.T.conj()) / 2
|
||||
s1, s1d = ss[i], ss[j]
|
||||
ss[i], ss[j] = (s1 + s1d.T.conj()) / 2, (s1d + s1.T.conj()) / 2
|
||||
|
||||
# identifying TRS and TRB parts of the Hamiltonian
|
||||
TAUY = np.kron(np.eye(NO), tau_y)
|
||||
hTR = np.array([TAUY @ hh[i].conj() @ TAUY for i in range(dh.lattice.nsc.prod())])
|
||||
hTRS = (hh + hTR) / 2
|
||||
hTRB = (hh - hTR) / 2
|
||||
|
||||
# extracting the exchange field
|
||||
traced = [spin_tracer(hTRB[i]) for i in range(dh.lattice.nsc.prod())] # equation 77
|
||||
XCF = np.array(
|
||||
[
|
||||
np.array([f["x"] for f in traced]),
|
||||
np.array([f["y"] for f in traced]),
|
||||
np.array([f["z"] for f in traced]),
|
||||
]
|
||||
) # equation 77
|
||||
|
||||
# Check if exchange field has scalar part
|
||||
max_xcfs = abs(np.array(np.array([f["c"] for f in traced]))).max()
|
||||
if max_xcfs > 1e-12:
|
||||
warnings.warn(
|
||||
f"Exchange field has non negligible scalar part. Largest value is {max_xcfs}"
|
||||
)
|
||||
|
||||
H_and_XCF_time = timer()
|
||||
|
||||
# for every site we have to store 3 Greens function (and the associated _tmp-s) in the 3 reference directions
|
||||
for i, mag_ent in enumerate(magnetic_entities):
|
||||
parsed = parse_magnetic_entity(dh, **mag_ent) # parse orbital indexes
|
||||
magnetic_entities[i]["orbital_indeces"] = parsed
|
||||
magnetic_entities[i]["spin_box_indeces"] = blow_up_orbindx(
|
||||
parsed
|
||||
) # calculate spin box indexes
|
||||
spin_box_shape = len(
|
||||
mag_ent["spin_box_indeces"]
|
||||
) # calculate size for Greens function generation
|
||||
|
||||
mag_ent["energies"] = [] # we will store the second order energy derivations here
|
||||
|
||||
mag_ent["Gii"] = [] # Greens function
|
||||
mag_ent["Gii_tmp"] = [] # Greens function for parallelization
|
||||
mag_ent["Vu1"] = [
|
||||
list([]) for _ in range(len(ref_xcf_orientations))
|
||||
] # These will be the perturbed potentials from eq. 100
|
||||
mag_ent["Vu2"] = [list([]) for _ in range(len(ref_xcf_orientations))]
|
||||
for i in ref_xcf_orientations:
|
||||
mag_ent["Gii"].append(
|
||||
np.zeros((eset, spin_box_shape, spin_box_shape), dtype="complex128")
|
||||
) # Greens functions for every quantization axis
|
||||
mag_ent["Gii_tmp"].append(
|
||||
np.zeros((eset, spin_box_shape, spin_box_shape), dtype="complex128")
|
||||
)
|
||||
|
||||
# for every site we have to store 2x3 Greens function (and the associated _tmp-s)
|
||||
# in the 3 reference directions, because G_ij and G_ji are both needed
|
||||
for pair in pairs:
|
||||
spin_box_shape_i, spin_box_shape_j = len(
|
||||
magnetic_entities[pair["ai"]]["spin_box_indeces"]
|
||||
), len(
|
||||
magnetic_entities[pair["aj"]]["spin_box_indeces"]
|
||||
) # calculate size for Greens function generation
|
||||
|
||||
pair["energies"] = [] # we will store the second order energy derivations here
|
||||
|
||||
pair["Gij"] = [] # Greens function
|
||||
pair["Gji"] = []
|
||||
pair["Gij_tmp"] = [] # Greens function for parallelization
|
||||
pair["Gji_tmp"] = []
|
||||
|
||||
pair["Vij"] = [
|
||||
list([]) for _ in range(len(ref_xcf_orientations))
|
||||
] # These will be the perturbed potentials from eq. 100
|
||||
pair["Vji"] = [list([]) for _ in range(len(ref_xcf_orientations))]
|
||||
|
||||
for i in ref_xcf_orientations:
|
||||
pair["Gij"].append(
|
||||
np.zeros((eset, spin_box_shape_i, spin_box_shape_j), dtype="complex128")
|
||||
)
|
||||
pair["Gij_tmp"].append(
|
||||
np.zeros((eset, spin_box_shape_i, spin_box_shape_j), dtype="complex128")
|
||||
) # Greens functions for every quantization axis
|
||||
pair["Gji"].append(
|
||||
np.zeros((eset, spin_box_shape_j, spin_box_shape_i), dtype="complex128")
|
||||
)
|
||||
pair["Gji_tmp"].append(
|
||||
np.zeros((eset, spin_box_shape_j, spin_box_shape_i), dtype="complex128")
|
||||
)
|
||||
|
||||
site_and_pair_dictionaries_time = timer()
|
||||
|
||||
kset = make_kset(dirs=kdirs, NUMK=kset) # generate k space sampling
|
||||
wkset = np.ones(len(kset)) / len(kset) # generate weights for k points
|
||||
kpcs = np.array_split(kset, size) # split the k points based on MPI size
|
||||
kpcs[root_node] = tqdm(kpcs[root_node], desc="k loop", file=stdout)
|
||||
|
||||
k_set_time = timer()
|
||||
|
||||
# this will contain all the data needed to calculate the energy variations upon rotation
|
||||
hamiltonians = []
|
||||
|
||||
# iterate over the reference directions (quantization axes)
|
||||
for i, orient in enumerate(ref_xcf_orientations):
|
||||
# obtain rotated exchange field
|
||||
R = RotMa2b(scf_xcf_orientation, orient["o"])
|
||||
rot_XCF = np.einsum("ij,jklm->iklm", R, XCF)
|
||||
rot_H_XCF = sum(
|
||||
[np.kron(rot_XCF[i], tau) for i, tau in enumerate([tau_x, tau_y, tau_z])]
|
||||
)
|
||||
rot_H_XCF_uc = rot_H_XCF[uc_in_sc_idx]
|
||||
|
||||
# obtain total Hamiltonian with the rotated exchange field
|
||||
rot_H = hTRS + rot_H_XCF # equation 76
|
||||
|
||||
hamiltonians.append(
|
||||
dict(orient=orient["o"], H=rot_H, rotations=[])
|
||||
) # store orientation and rotated Hamiltonian
|
||||
|
||||
for u in orient[
|
||||
"vw"
|
||||
]: # these are the infinitezimal rotations (for now) perpendicular to the quantization axis
|
||||
Tu = np.kron(np.eye(NO, dtype=int), tau_u(u)) # section 2.H
|
||||
|
||||
Vu1 = 1j / 2 * commutator(rot_H_XCF_uc, Tu) # equation 100
|
||||
Vu2 = 1 / 8 * commutator(commutator(Tu, rot_H_XCF_uc), Tu) # equation 100
|
||||
|
||||
for mag_ent in magnetic_entities:
|
||||
mag_ent["Vu1"][i].append(
|
||||
Vu1[:, mag_ent["spin_box_indeces"]][mag_ent["spin_box_indeces"], :]
|
||||
) # fill up the perturbed potentials (for now) based on the on-site projections
|
||||
mag_ent["Vu2"][i].append(
|
||||
Vu2[:, mag_ent["spin_box_indeces"]][mag_ent["spin_box_indeces"], :]
|
||||
)
|
||||
|
||||
for pair in pairs:
|
||||
ai = magnetic_entities[pair["ai"]][
|
||||
"spin_box_indeces"
|
||||
] # get the pair orbital sizes from the magnetic entities
|
||||
aj = magnetic_entities[pair["aj"]]["spin_box_indeces"]
|
||||
pair["Vij"][i].append(
|
||||
Vu1[:, ai][aj, :]
|
||||
) # fill up the perturbed potentials (for now) based on the on-site projections
|
||||
pair["Vji"][i].append(Vu1[:, aj][ai, :])
|
||||
|
||||
reference_rotations_time = timer()
|
||||
|
||||
if rank == root_node:
|
||||
print("Number of magnetic entities being calculated: ", len(magnetic_entities))
|
||||
print(
|
||||
"We have to calculate the Greens function for three reference direction and we are going to calculate 15 energy integrals per site."
|
||||
)
|
||||
print(f"The shape of the Hamiltonian and the Greens function is {NO}x{NO}.")
|
||||
comm.Barrier()
|
||||
# ----------------------------------------------------------------------
|
||||
|
||||
# make energy contour
|
||||
# we are working in eV now !
|
||||
# and sisil shifts E_F to 0 !
|
||||
cont = make_contour(emin=ebot, enum=eset, p=esetp)
|
||||
eran = cont.ze
|
||||
|
||||
# ----------------------------------------------------------------------
|
||||
# sampling the integrand on the contour and the BZ
|
||||
for k in kpcs[rank]:
|
||||
wk = wkset[rank] # weight of k point in BZ integral
|
||||
for i, hamiltonian_orientation in enumerate(
|
||||
hamiltonians
|
||||
): # iterate over reference directions
|
||||
# calculate Greens function
|
||||
H = hamiltonian_orientation["H"]
|
||||
HK, SK = hsk(H, ss, dh.sc_off, k)
|
||||
Gk = inv(SK * eran.reshape(eset, 1, 1) - HK)
|
||||
|
||||
# store the Greens function slice of the magnetic entities (for now) based on the on-site projections
|
||||
for mag_ent in magnetic_entities:
|
||||
mag_ent["Gii_tmp"][i] += (
|
||||
Gk[:, mag_ent["spin_box_indeces"]][..., mag_ent["spin_box_indeces"]]
|
||||
* wk
|
||||
)
|
||||
|
||||
for pair in pairs:
|
||||
# add phase shift based on the cell difference
|
||||
phase = np.exp(1j * 2 * np.pi * k @ pair["Ruc"].T)
|
||||
|
||||
# get the pair orbital sizes from the magnetic entities
|
||||
ai = magnetic_entities[pair["ai"]]["spin_box_indeces"]
|
||||
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(print_atomic_indices(pair, magnetic_entities, dh))
|
||||
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