parent
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import numpy as np
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from numpy.linalg import inv
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from grogu_magn.utils import blow_up_orbindx, commutator, parse_magnetic_entity
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def parallel_Gk(HK, SK, eran, eset):
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return inv(SK * eran.reshape(eset, 1, 1) - HK)
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def sequential_GK(HK, SK, eran, eset):
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Gk = np.zeros(shape=(eset, HK.shape[0], HK.shape[1]), dtype="complex128")
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for j in range(eset):
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Gk[j] = inv(SK * eran[j] - HK)
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return Gk
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def calc_Vu(H, Tu):
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"""_summary_
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Args:
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H (_type_): _description_
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Tu (_type_): _description_
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Returns:
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_type_: _description_
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"""
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Vu1 = 1j / 2 * commutator(H, Tu) # equation 100
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Vu2 = 1 / 8 * commutator(commutator(Tu, H), Tu) # equation 100
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return Vu1, Vu2
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def remove_clutter_for_save(pairs, magnetic_entities):
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"""_summary_
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Args:
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pairs (_type_): _description_
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magnetic_entities (_type_): _description_
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Returns:
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_type_: _description_
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"""
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# remove clutter from magnetic entities and pair information
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for pair in pairs:
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del pair["Gij"]
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del pair["Gij_tmp"]
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del pair["Gji"]
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del pair["Gji_tmp"]
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for mag_ent in magnetic_entities:
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del mag_ent["Gii"]
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del mag_ent["Gii_tmp"]
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del mag_ent["Vu1"]
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del mag_ent["Vu2"]
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return pairs, magnetic_entities
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def build_hh_ss(dh):
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"""_summary_
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Args:
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dh (_type_): _description_
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Returns:
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_type_: _description_
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"""
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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
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@ np.block([[h11[:, :, i], h12[:, :, i]], [h21[:, :, i], h22[:, :, 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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), np.array(
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[
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U.T
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@ np.block(
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[[sov[:, :, i], sov[:, :, i] * 0], [sov[:, :, i] * 0, sov[:, :, i]]]
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)
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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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return hh, ss, NO
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def setup_pairs_and_magnetic_entities(
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magnetic_entities, pairs, dh, simulation_parameters
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):
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"""_summary_
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Args:
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magnetic_entities (_type_): _description_
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pairs (_type_): _description_
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dh (_type_): _description_
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simulation_parameters (_type_): _description_
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Returns:
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_type_: _description_
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"""
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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 mag_ent in magnetic_entities:
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parsed = parse_magnetic_entity(dh, **mag_ent) # parse orbital indexes
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mag_ent["orbital_indeces"] = parsed
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mag_ent["spin_box_indeces"] = blow_up_orbindx(
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parsed
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) # calculate spin box indexes
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# if orbital is not set use all
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if "l" not in mag_ent.keys():
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mag_ent["l"] = "all"
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if isinstance(mag_ent["atom"], int):
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mag_ent["tags"] = [
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f"[{mag_ent['atom']}]{dh.atoms[mag_ent['atom']].tag}({mag_ent['l']})"
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]
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mag_ent["xyz"] = [dh.xyz[mag_ent["atom"]]]
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if isinstance(mag_ent["atom"], list):
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mag_ent["tags"] = []
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mag_ent["xyz"] = []
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# iterate over atoms
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for atom_idx in mag_ent["atom"]:
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mag_ent["tags"].append(
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f"[{atom_idx}]{dh.atoms[atom_idx].tag}({mag_ent['l']})"
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)
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mag_ent["xyz"].append(dh.xyz[atom_idx])
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# calculate size for Greens function generation
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spin_box_shape = len(mag_ent["spin_box_indeces"])
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mag_ent["energies"] = (
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[]
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) # we will store the second order energy derivations here
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# These will be the perturbed potentials from eq. 100
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mag_ent["Vu1"] = [] # so they are independent in memory
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mag_ent["Vu2"] = []
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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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for i in simulation_parameters["ref_xcf_orientations"]:
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# Rotations for every quantization axis
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mag_ent["Vu1"].append([])
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mag_ent["Vu2"].append([])
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# Greens functions for every quantization axis
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mag_ent["Gii"].append(
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np.zeros(
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(simulation_parameters["eset"], spin_box_shape, spin_box_shape),
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dtype="complex128",
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)
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)
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mag_ent["Gii_tmp"].append(
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np.zeros(
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(simulation_parameters["eset"], spin_box_shape, spin_box_shape),
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dtype="complex128",
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)
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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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# calculate distance
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xyz_ai = magnetic_entities[pair["ai"]]["xyz"]
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xyz_aj = magnetic_entities[pair["aj"]]["xyz"]
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xyz_aj = xyz_aj + pair["Ruc"] @ simulation_parameters["cell"]
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pair["dist"] = np.linalg.norm(xyz_ai - xyz_aj)
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# calculate size for Greens function generation
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spin_box_shape_i = len(magnetic_entities[pair["ai"]]["spin_box_indeces"])
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spin_box_shape_j = len(magnetic_entities[pair["aj"]]["spin_box_indeces"])
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pair["tags"] = []
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for mag_ent in [magnetic_entities[pair["ai"]], magnetic_entities[pair["aj"]]]:
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tag = ""
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# get atoms of magnetic entity
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atoms_idx = mag_ent["atom"]
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orbitals = mag_ent["l"]
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# if magnetic entity contains one atoms
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if isinstance(atoms_idx, int):
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tag += f"[{atoms_idx}]{dh.atoms[atoms_idx].tag}({orbitals})"
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# if magnetic entity contains more than one atoms
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if isinstance(atoms_idx, list):
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# iterate over atoms
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atom_group = "{"
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for atom_idx in atoms_idx:
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atom_group += f"[{atom_idx}]{dh.atoms[atom_idx].tag}({orbitals})--"
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# end {} of the atoms in the magnetic entity
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tag += atom_group[:-2] + "}"
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pair["tags"].append(tag)
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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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for i in simulation_parameters["ref_xcf_orientations"]:
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# Greens functions for every quantization axis
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pair["Gij"].append(
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np.zeros(
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(simulation_parameters["eset"], spin_box_shape_i, spin_box_shape_j),
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dtype="complex128",
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)
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)
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pair["Gij_tmp"].append(
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np.zeros(
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(simulation_parameters["eset"], spin_box_shape_i, spin_box_shape_j),
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dtype="complex128",
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)
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)
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pair["Gji"].append(
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np.zeros(
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(simulation_parameters["eset"], spin_box_shape_j, spin_box_shape_i),
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dtype="complex128",
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)
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)
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pair["Gji_tmp"].append(
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np.zeros(
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(simulation_parameters["eset"], spin_box_shape_j, spin_box_shape_i),
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dtype="complex128",
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)
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)
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return pairs, magnetic_entities
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@ -0,0 +1,19 @@
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# Copyright (c) [2024] [Daniel Pozsar]
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#
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# Permission is hereby granted, free of charge, to any person obtaining a copy
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# of this software and associated documentation files (the "Software"), to deal
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# in the Software without restriction, including without limitation the rights
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# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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# copies of the Software, and to permit persons to whom the Software is
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# furnished to do so, subject to the following conditions:
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#
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# The above copyright notice and this permission notice shall be included in all
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# copies or substantial portions of the Software.
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#
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# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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# SOFTWARE.
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@ -0,0 +1,219 @@
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from argparse import ArgumentParser
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from pickle import dump, load
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import numpy as np
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default_args = dict(
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infile=None,
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outfile=None,
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scf_xcf_orientation=np.array([0, 0, 1]),
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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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kset=2,
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kdirs="xyz",
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ebot=None,
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eset=42,
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esetp=1000,
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)
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# parser = ArgumentParser()
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# parser.add_argument('--input' , dest = 'infile' , default=None , help = 'Input file name')
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# parser.add_argument('--output' , dest = 'outfile', default=None , help = 'Output file name')
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# parser.add_argument('--kset' , dest = 'kset' , default = 2 , type=int , help = 'k-space resolution of Jij calculation')
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# parser.add_argument('--kdirs' , dest = 'kdirs' , default = 'xyz' , help = 'Definition of k-space dimensionality')
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# parser.add_argument('--ebot' , dest = 'ebot' , default = None , type=float, help = 'Bottom energy of the contour')
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# parser.add_argument('--eset' , dest = 'eset' , default = 42 , type=int , help = 'Number of energy points on the contour')
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# parser.add_argument('--eset-p' , dest = 'esetp' , default = 1000 , type=int , help = 'Parameter tuning the distribution on the contour')
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# cmd_line_args = parser.parse_args()
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def save_pickle(outfile, data):
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"""_summary_
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Args:
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outfile (_type_): _description_
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data (_type_): _description_
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"""
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# save dictionary
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with open(outfile, "wb") as output_file:
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dump(data, output_file)
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def load_pickle(infile, data):
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"""_summary_
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Args:
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infile (_type_): _description_
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data (_type_): _description_
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Returns:
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_type_: _description_
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"""
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with open(infile, "wb") as input_file:
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data = load(data, input_file)
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return data
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def print_parameters(simulation_parameters):
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"""_summary_
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Args:
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simulation_parameters (_type_): _description_
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"""
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print(
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"================================================================================================================================================================"
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)
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print("Input file: ")
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print(simulation_parameters["infile"])
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print("Output file: ")
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print(simulation_parameters["outfile"])
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print(
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"Number of nodes in the parallel cluster: ",
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simulation_parameters["parallel_size"],
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)
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print(
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"================================================================================================================================================================"
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)
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print("Cell [Ang]: ")
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print(simulation_parameters["cell"])
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print(
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"================================================================================================================================================================"
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)
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print("DFT axis: ")
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print(simulation_parameters["scf_xcf_orientation"])
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print("Quantization axis and perpendicular rotation directions:")
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for ref in simulation_parameters["ref_xcf_orientations"]:
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print(ref["o"], " --» ", ref["vw"])
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print(
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"================================================================================================================================================================"
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)
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print("Parameters for the contour integral:")
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print("Number of k points: ", simulation_parameters["kset"])
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print("k point directions: ", simulation_parameters["kdirs"])
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print("Ebot: ", simulation_parameters["ebot"])
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print("Eset: ", simulation_parameters["eset"])
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print("Esetp: ", simulation_parameters["esetp"])
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print(
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"================================================================================================================================================================"
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)
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def print_atoms_and_pairs(magnetic_entities, pairs):
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"""_summary_
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Args:
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magnetic_entities (_type_): _description_
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pairs (_type_): _description_
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"""
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print("Atomic information: ")
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print(
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"----------------------------------------------------------------------------------------------------------------------------------------------------------------"
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)
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print(
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"[atom index]Element(orbitals) x [Ang] y [Ang] z [Ang] Sx Sy Sz Q Lx Ly Lz Jx Jy Jz"
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)
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print(
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"----------------------------------------------------------------------------------------------------------------------------------------------------------------"
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)
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# iterate over magnetic entities
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for mag_ent in magnetic_entities:
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# iterate over atoms
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for tag, xyz in zip(mag_ent["tags"], mag_ent["xyz"]):
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# coordinates and tag
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print(f"{tag} {xyz[0]} {xyz[1]} {xyz[2]}")
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print("")
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print(
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"================================================================================================================================================================"
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)
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print("Anisotropy [meV]")
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print(
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"----------------------------------------------------------------------------------------------------------------------------------------------------------------"
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)
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print("Magnetic entity x [Ang] y [Ang] z [Ang]")
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print(
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"----------------------------------------------------------------------------------------------------------------------------------------------------------------"
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)
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# iterate over magnetic entities
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for mag_ent in magnetic_entities:
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# iterate over atoms
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for tag, xyz in zip(mag_ent["tags"], mag_ent["xyz"]):
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# coordinates and tag
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print(f"{tag} {xyz[0]} {xyz[1]} {xyz[2]}")
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print("Consistency check: ", mag_ent["K_consistency"])
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print("Anisotropy diag: ", mag_ent["K"])
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print("")
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print(
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"================================================================================================================================================================"
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)
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print("Exchange [meV]")
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print(
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"----------------------------------------------------------------------------------------------------------------------------------------------------------------"
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)
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print("Magnetic entity1 Magnetic entity2 [i j k] d [Ang]")
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print(
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"----------------------------------------------------------------------------------------------------------------------------------------------------------------"
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)
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# iterate over pairs
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for pair in pairs:
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# print pair parameters
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print(
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f"{pair['tags'][0]} {pair['tags'][1]} {pair['Ruc']} d [Ang] {pair['dist']}"
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)
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# print magnetic parameters
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print("Isotropic: ", pair["J_iso"])
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print("DMI: ", pair["D"])
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print("Symmetric-anisotropy: ", pair["J_S"])
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print("J: ", pair["J"].flatten())
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print("Energies for debugging: ")
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print(np.array(pair["energies"]))
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print(
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"J_ii for debugging: (check if this is the same as in calculate_exchange_tensor)"
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)
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o1, o2, o3 = pair["energies"]
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print(np.array([o2[-1], o3[0], o1[0]]))
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print("Test J_xx = E(y,z) = E(z,y)")
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print(o2[-1], o3[-1])
|
||||
print("")
|
||||
|
||||
print(
|
||||
"================================================================================================================================================================"
|
||||
)
|
||||
|
||||
|
||||
def print_runtime_information(times):
|
||||
"""_summary_
|
||||
|
||||
Args:
|
||||
times (_type_): _description_
|
||||
"""
|
||||
print("Runtime information: ")
|
||||
print(f"Total runtime: {times['end_time'] - times['start_time']} s")
|
||||
print(
|
||||
"----------------------------------------------------------------------------------------------------------------------------------------------------------------"
|
||||
)
|
||||
print(f"Initial setup: {times['setup_time'] - times['start_time']} s")
|
||||
print(
|
||||
f"Hamiltonian conversion and XC field extraction: {times['H_and_XCF_time'] - times['setup_time']:.3f} s"
|
||||
)
|
||||
print(
|
||||
f"Pair and site datastructure creatrions: {times['site_and_pair_dictionaries_time'] - times['H_and_XCF_time']:.3f} s"
|
||||
)
|
||||
print(
|
||||
f"k set cration and distribution: {times['k_set_time'] - times['site_and_pair_dictionaries_time']:.3f} s"
|
||||
)
|
||||
print(
|
||||
f"Rotating XC potential: {times['reference_rotations_time'] - times['k_set_time']:.3f} s"
|
||||
)
|
||||
print(
|
||||
f"Greens function inversion: {times['green_function_inversion_time'] - times['reference_rotations_time']:.3f} s"
|
||||
)
|
||||
print(
|
||||
f"Calculate energies and magnetic components: {times['end_time'] - times['green_function_inversion_time']:.3f} s"
|
||||
)
|
||||
@ -0,0 +1,88 @@
|
||||
import numpy as np
|
||||
|
||||
|
||||
def calculate_anisotropy_tensor(mag_ent):
|
||||
"""_summary_
|
||||
|
||||
Args:
|
||||
mag_ent (_type_): _description_
|
||||
|
||||
Returns:
|
||||
_type_: _description_
|
||||
"""
|
||||
|
||||
energies = mag_ent["energies"]
|
||||
Kxx = energies[1, 1] - energies[1, 0]
|
||||
Kyy = energies[0, 1] - energies[0, 0]
|
||||
Kzz = 0
|
||||
|
||||
calculated_diff = Kyy - Kxx
|
||||
expected_diff = energies[2, 0] - energies[2, 1]
|
||||
consistency_check = abs(calculated_diff - expected_diff)
|
||||
|
||||
return Kxx, Kyy, Kzz, consistency_check
|
||||
|
||||
|
||||
def calculate_exchange_tensor(pair):
|
||||
"""_summary_
|
||||
|
||||
Args:
|
||||
pair (_type_): _description_
|
||||
|
||||
Returns:
|
||||
_type_: _description_
|
||||
"""
|
||||
energies = pair["energies"]
|
||||
# Initialize output arrays
|
||||
J = np.zeros((3, 3))
|
||||
D = np.zeros(3)
|
||||
|
||||
# J matrix calculations
|
||||
# J(1,1) = mean([DEij(2,2,2), DEij(2,2,3)])
|
||||
J[0, 0] = np.mean([energies[1, 3], energies[2, 3]])
|
||||
|
||||
# J(1,2) = -mean([DEij(1,2,3), DEij(2,1,3)])
|
||||
J[0, 1] = -np.mean([energies[2, 1], energies[2, 2]])
|
||||
J[1, 0] = J[0, 1]
|
||||
|
||||
# J(1,3) = -mean([DEij(1,2,2), DEij(2,1,2)])
|
||||
J[0, 2] = -np.mean([energies[1, 1], energies[1, 2]])
|
||||
J[2, 0] = J[0, 2]
|
||||
|
||||
# J(2,2) = mean([DEij(2,2,1), DEij(1,1,3)])
|
||||
J[1, 1] = np.mean([energies[0, 3], energies[2, 0]])
|
||||
|
||||
# J(2,3) = -mean([DEij(1,2,1), DEij(2,1,1)])
|
||||
J[1, 2] = -np.mean([energies[0, 1], energies[0, 2]])
|
||||
J[2, 1] = J[1, 2]
|
||||
|
||||
# J(3,3) = mean([DEij(1,1,1), DEij(1,1,2)])
|
||||
J[2, 2] = np.mean([energies[0, 0], energies[1, 0]])
|
||||
|
||||
# D vector calculations
|
||||
# D(1) = mean([DEij(1,2,1), -DEij(2,1,1)])
|
||||
D[0] = np.mean([energies[0, 1], -energies[0, 2]])
|
||||
|
||||
# D(2) = mean([DEij(2,1,2), -DEij(1,2,2)])
|
||||
D[1] = np.mean([energies[1, 2], -energies[1, 1]])
|
||||
|
||||
# D(3) = mean([DEij(1,2,3), -DEij(2,1,3)])
|
||||
D[2] = np.mean([energies[2, 1], -energies[2, 2]])
|
||||
|
||||
J_iso = np.trace(J) / 3
|
||||
J_S = (J - J_iso * np.eye(3)).flatten()
|
||||
|
||||
return J_iso, J_S, D, J
|
||||
|
||||
|
||||
def int_de_ke(traced, we):
|
||||
"""_summary_
|
||||
|
||||
Args:
|
||||
traced (_type_): _description_
|
||||
we (_type_): _description_
|
||||
|
||||
Returns:
|
||||
_type_: _description_
|
||||
"""
|
||||
return np.trapz(-1 / np.pi * np.imag(traced * we))
|
||||
Loading…
Reference in new issue