def set_tbmodels(self, tbmodels):
"""
only difference is a colinear tag.
"""
self.tbmodel_up, self.tbmodel_dn = tbmodels
self.Gup = TBGreen(self.tbmodel_up,
self.kmesh,
self.efermi,
use_cache=self._use_cache,
cache_path='TB2J_results/cache/spinup')
self.Gdn = TBGreen(self.tbmodel_dn,
self.kmesh,
self.efermi,
use_cache=self._use_cache,
cache_path='TB2J_results/cache/spindn')
self.norb = self.Gup.norb
self.nbasis = self.Gup.nbasis + self.Gdn.nbasis
self.rho_up = np.zeros((self.norb, self.norb), dtype=float)
self.rho_dn = np.zeros((self.norb, self.norb), dtype=float)
self.JJ = defaultdict(lambda: 0.0j)
self.Jorb = defaultdict(lambda: 0.0j)
self.HR0_up = self.Gup.H0
self.HR0_dn = self.Gdn.H0
self.Delta = self.HR0_up - self.HR0_dn
if self.Gup.is_orthogonal and self.Gdn.is_orthogonal:
self.is_orthogonal = True
else:
self.is_orthogonal = False
#self.S0=self.Gup.S0
self._is_colinear = True
self.exchange_Jdict = {}
self.exchange_Jdict_orb = {}
self.biquadratic = False
def set_tbmodels(self, tbmodels):
"""
tbmodels should be in spinor form.
The basis should be orb1_up, orb2_up,...orbn_up, orb1_dn, orb2_dn....
"""
self.tbmodel = tbmodels
# TODO: check if tbmodels are really a tbmodel with SOC.
self.G = TBGreen(self.tbmodel, self.kmesh, self.efermi)
self.norb = self.G.norb
self.nbasis = self.G.nbasis
self.rho = np.zeros((self.nbasis, self.nbasis), dtype=float)
self.A_ijR = defaultdict(lambda: np.zeros((4, 4), dtype=complex))
#self.HR0 = self.tbmodel.ham_R0
self.HR0 = self.G.H0
if not self.G.is_orthogonal:
self.S0 = self.G.S0
self._is_collinear = False
self.Pdict = {}
def set_tbmodels(self, tbmodels):
"""
tbmodels should be in spinor form.
The basis should be orb1_up, orb2_up,...orbn_up, orb1_dn, orb2_dn....
"""
self.tbmodel = tbmodels
# TODO: check if tbmodels are really a tbmodel with SOC.
self.G = TBGreen(self.tbmodel,
self.kmesh,
self.efermi,
use_cache=self._use_cache,
nproc=self.np)
self.norb = self.G.norb
self.nbasis = self.G.nbasis
self.rho = np.zeros((self.nbasis, self.nbasis), dtype=complex)
self.A_ijR_list = defaultdict(lambda: [])
self.A_ijR = defaultdict(lambda: np.zeros((4, 4), dtype=complex))
self.HR0 = self.G.H0
self._is_collinear = False
self.Pdict = {}
class ExchangeNCL(Exchange):
"""
Non-collinear exchange
"""
def set_tbmodels(self, tbmodels):
"""
tbmodels should be in spinor form.
The basis should be orb1_up, orb2_up,...orbn_up, orb1_dn, orb2_dn....
"""
self.tbmodel = tbmodels
# TODO: check if tbmodels are really a tbmodel with SOC.
self.G = TBGreen(self.tbmodel, self.kmesh, self.efermi)
self.norb = self.G.norb
self.nbasis = self.G.nbasis
self.rho = np.zeros((self.nbasis, self.nbasis), dtype=float)
self.A_ijR = defaultdict(lambda: np.zeros((4, 4), dtype=complex))
#self.HR0 = self.tbmodel.ham_R0
self.HR0 = self.G.H0
if not self.G.is_orthogonal:
self.S0 = self.G.S0
self._is_collinear = False
self.Pdict = {}
def _prepare_NijR(self):
self.N = {}
for R in self.Rlist:
self.N[R] = np.zeros((self.nbasis, self.nbasis), dtype=complex)
def _prepare_Patom(self):
for iatom in self.ind_mag_atoms:
self.Pdict[iatom] = pauli_block_sigma_norm(self.get_H_atom(iatom))
def get_H_atom(self, iatom):
orbs = self.iorb(iatom)
return self.HR0[np.ix_(orbs, orbs)]
def get_P_iatom(self, iatom):
""" Calculate the norm of the Hamiltonian vector.
For each atom, the local hamiltonian of each orbital H(2*2 matrix)
can be written as H0* I + H1* sigma1 + H2*sigma2 + H3 *sigma3
where sigma is a Pauli matrix. return the norm of (H1, H2, H3) vector
:param iatom: index of atom
:returns: a matrix of norms P. P[i, j] is for orbital i and j.
:rtype: complex matrix of shape norb_i * norb_i.
"""
if self.Pdict == {}:
self._prepare_Patom()
return self.Pdict[iatom]
def GR_atom(self, GR, iatom, jatom):
"""Given a green's function matrix, return the [iatom, jatom] component.
:param GR: Green's function matrix
:param iatom: index of atom i
:param jatom: index of atom j
:returns: G_ij
:rtype: complex matrix.
"""
orbi = self.iorb(iatom)
orbj = self.iorb(jatom)
return GR[np.ix_(orbi, orbj)]
def get_A_ijR(self, G, iatom, jatom, de):
""" calculate A from G for a energy slice (de).
It take the
.. math::
A^{uv} = p T^u p T^v dE / pi
where u, v are I, x, y, z (index 0, 1,2,3). p(i) = self.get_P_iatom(iatom)
T^u(ijR) (u=0,1,2,3) = pauli_block_all(G)
:param G: Green's function for all R, i, j.
:param iatom: i
:param jatom: j
:param de: energy step. used for integeration
:returns: a matrix of A_ij(u, v), where u, v =(0)0, x(1), y(2), z(3)
:rtype: 4*4 matrix
"""
for R in self.R_ijatom_dict:
# G[i, j, R]
GR = G[R]
if (iatom, jatom) in self.R_ijatom_dict[R]:
Gij = self.GR_atom(GR, iatom, jatom)
# GijR , I, x, y, z component.
Gij_Ixyz = pauli_block_all(Gij)
# G(j, i, -R)
Rm = tuple(-x for x in R)
GRm = G[Rm]
Gji = self.GR_atom(GRm, jatom, iatom)
Gji_Ixyz = pauli_block_all(Gji)
tmp = np.zeros((4, 4), dtype=complex)
for a in range(4):
for b in range(4):
AijRab = np.matmul(
np.matmul(self.get_P_iatom(iatom), Gij_Ixyz[a]),
np.matmul(self.get_P_iatom(jatom), Gji_Ixyz[b]))
# trace over orb
tmp[a, b] = np.trace(AijRab)
# Note: the full complex, rather than Re or Im part is stored into A_ijR.
self.A_ijR[(R, iatom, jatom)] += tmp * de / np.pi
def get_all_A(self, G, de):
"""
Calculate all A matrix elements
Loop over all magnetic atoms.
:param G: Green's function.
:param de: energy step.
"""
for iatom in self.ind_mag_atoms:
for jatom in self.ind_mag_atoms:
self.get_A_ijR(G, iatom, jatom, de)
def A_to_Jtensor(self):
"""
Calculate J tensors from A.
If we assume the exchange can be written as a bilinear tensor form,
J_{isotropic} = Tr Im (A^{00} - A^{xx} - A^{yy} - A^{zz})
J_{anisotropic}_uv = Tr Im (2A)
DMI = Tr Re (A^{0z} - A^{z0} )
"""
self.Jani = {}
self.DMI = {}
self.Jprime = {}
self.B = {}
self.exchange_Jdict = {}
for key, val in self.A_ijR.items():
# key:(R, iatom, jatom)
R, iatom, jatom = key
Rm = tuple(-x for x in R)
valm = self.A_ijR[(Rm, jatom, iatom)]
ispin = self.ispin(iatom)
jspin = self.ispin(jatom)
keyspin = (R, ispin, jspin)
is_nonself = not (R == (0, 0, 0) and iatom == jatom)
Jiso = np.zeros((3, 3), dtype=float)
Ja = np.zeros((3, 3), dtype=float)
Dtmp = np.zeros(3, dtype=float)
# Heisenberg like J.
for i in range(3):
Jiso[i, i] += np.imag(val[0, 0] - val[1, 1] - val[2, 2] -
val[3, 3])
#Jiso[i, i] += np.imag(val[0, 0] - val[3, 3])
if is_nonself:
self.exchange_Jdict[keyspin] = Jiso[0, 0]
# off-diagonal ansiotropic exchange
for i in range(3):
for j in range(3):
if i != j:
#Ja[i,j] = np.imag(val[i + 1, j + 1] + valm[i + 1, j + 1])
Ja[i, j] = -np.imag(val[i + 1, j + 1] +
valm[i + 1, j + 1]) / 2.0
#Ja[i,j] = -np.imag(val[i+1, j+1])
if is_nonself:
self.Jani[keyspin] = Ja
# DMI
for i in range(3):
Dtmp[i] = np.real(val[0, i + 1] - val[i + 1, 0])
# Dx = Jyz-Jzy
# Dy = Jzx-Jxz
# Dz = Jxy-Jyx
#Dtmp[0] = np.imag(val[2, 3] - val[3, 2])
#Dtmp[1] = np.imag(val[3, 1] - val[1, 3])
#Dtmp[2] = np.imag(val[1, 2] - val[2, 1])
if is_nonself:
self.DMI[keyspin] = Dtmp
# isotropic exchange into bilinear and biqudratic parts:
# Jprime SiSj and B (SiSj)^2
if is_nonself:
Si = self.spinat[iatom]
Sj = self.spinat[jatom]
Jprime = np.imag(val[0, 0] - val[3, 3]) - 2 * np.sign(
np.dot(Si, Sj)) * np.imag(val[3, 3])
#Jprime = np.imag(val[0, 0] - 3*val[3, 3])
B = np.imag(val[3, 3])
self.B[keyspin] = Jprime, B
def get_N_e(self, GR, de):
"""
calcualte density matrix for all R,i, j
"""
self.N=defaultdict(lambda: 0.0)
for R, G in GR.items():
self.N[R] += -1.0 / np.pi * np.imag(G * de)
def get_rho_e(self, rhoR, de):
""" add component to density matrix from a green's function
:param GR: Green's funciton in real space.
:param de: energy step
"""
#GR0 = GR[(0, 0, 0)]
#if self.G.is_orthogonal:
# self.rho += -1.0 / np.pi * np.imag(GR0 * de)
#else:
# self.rho += -1.0 / np.pi * np.imag(self.S0@GR0 * de)
self.rho += -1.0 / np.pi * np.imag(rhoR[0, 0, 0] * de)
def get_total_charges(self):
return np.sum(np.real(np.diag(self.rho)))
def get_rho_atom(self):
"""
calculate charge and spin for each atom.
"""
rho = {}
self.charges = np.zeros(len(self.atoms), dtype=float)
self.spinat = np.zeros((len(self.atoms), 3), dtype=float)
for iatom in self.orb_dict:
iorb = self.iorb(iatom)
tmp = self.rho[np.ix_(iorb, iorb)]
# *2 because there is a 1/2 in the paui_block_all function
rho[iatom] = np.array(
[np.trace(x) * 2 for x in pauli_block_all(tmp)])
self.charges[iatom] = np.real(rho[iatom][0])
self.spinat[iatom, :] = np.real(rho[iatom][1:])
self.rho_dict = rho
return self.rho_dict
def calculate_DMI_NJT(self):
"""
calculate exchange and DMI with the
D(i,j) =
"""
Ddict_NJT = {}
Jdict_NJT = {}
for R in self.short_Rlist:
N = self.N[tuple(-np.array(R))] # density matrix
t = self.tbmodel.get_hamR(R) # hopping parameter
for iatom in self.ind_mag_atoms:
orbi = self.iorb(iatom)
ni = len(orbi)
for jatom in self.ind_mag_atoms:
orbj = self.iorb(jatom)
nj = len(orbj)
Nji = N[np.ix_(orbj, orbi)]
tij = t[np.ix_(orbi, orbj)]
D = np.zeros(3, dtype=float)
J = np.zeros(3, dtype=float)
for dim in range(3):
#S_i = pauli_mat(ni, dim +
# 1) #*self.rho[np.ix_(orbi, orbi)]
#S_j = pauli_mat(nj, dim +
# 1) #*self.rho[np.ix_(orbj, orbj)]
S_i = pauli_mat(ni, dim +
1) *self.rho[np.ix_(orbi, orbi)]
S_j = pauli_mat(nj, dim +
1) *self.rho[np.ix_(orbj, orbj)]
# [S, t]+ = Si tij + tij Sj, where
# Si and Sj are the spin operator
# Here we do not have L operator, so J-> S
Jt = np.matmul(S_i, tij) + np.matmul(tij, S_j)
Jtminus = np.matmul(S_i, tij) - np.matmul(tij, S_j)
# D = -1/2 Tr Nji [J, tij]
# Trace over spin and orb
D[dim] = -0.5 * np.imag(np.trace(np.matmul(Nji, Jt)))
J[dim] = -0.5 * np.imag(
np.trace(np.matmul(Nji, Jtminus)))
ispin = self.ispin(iatom)
jspin = self.ispin(jatom)
Ddict_NJT[(R, ispin, jspin)] = D
Jdict_NJT[(R, ispin, jspin)] = J
self.Jdict_NJT = Jdict_NJT
self.Ddict_NJT = Ddict_NJT
return Ddict_NJT
def calculate_all(self):
"""
The top level.
"""
print("Green's function Calculation started.")
widgets = [
' [',
progressbar.Timer(),
'] ',
progressbar.Bar(),
' (',
progressbar.ETA(),
') ',
]
bar = progressbar.ProgressBar(maxval=self.contour.npoints,
widgets=widgets)
bar.start()
for ie in range(self.contour.npoints):
bar.update(ie)
#if self.ne is not none and self.get_total_charges(
#) > self.ne and ie not in self.elistc:
# self._prepare_elistc(self, ie)
# continue
e = self.contour.path[ie]
de = self.contour.de[ie]
GR, rhoR = self.G.get_GR(self.short_Rlist, energy=e, get_rho=True)
self.get_rho_e(rhoR, de)
self.get_all_A(GR, de)
if self.calc_NJt:
self.get_N_e(GR, de)
self.get_rho_atom()
self.A_to_Jtensor()
#self.calculate_DMI_NJT()
bar.finish()
def _prepare_index_spin(self):
# index_spin: index in spin hamiltonian of atom. starts from 1. -1 means not considered.
ind_matoms = []
self.index_spin = []
ispin = 0
for i, sym in enumerate(self.atoms.get_chemical_symbols()):
if sym in self.magnetic_elements:
ind_matoms.append(i)
self.index_spin.append(ispin)
ispin += 1
else:
self.index_spin.append(-1)
def write_output(self, path='TB2J_results'):
self._prepare_index_spin()
output = SpinIO(
atoms=self.atoms,
charges=self.charges,
spinat=self.spinat,
index_spin=self.index_spin,
colinear=False,
distance_dict=self.distance_dict,
exchange_Jdict=self.exchange_Jdict,
dmi_ddict=self.DMI,
NJT_Jdict=self.Jdict_NJT,
NJT_ddict=self.Ddict_NJT,
Jani_dict=self.Jani,
biquadratic_Jdict=self.B,
)
output.write_all(path=path)
def run(self, path='TB2J_results'):
self.calculate_all()
self.write_output(path=path)
class ExchangeCL2(ExchangeCL):
def set_tbmodels(self, tbmodels):
"""
only difference is a colinear tag.
"""
self.tbmodel_up, self.tbmodel_dn = tbmodels
self.Gup = TBGreen(self.tbmodel_up,
self.kmesh,
self.efermi,
use_cache=self._use_cache,
cache_path='TB2J_results/cache/spinup')
self.Gdn = TBGreen(self.tbmodel_dn,
self.kmesh,
self.efermi,
use_cache=self._use_cache,
cache_path='TB2J_results/cache/spindn')
self.norb = self.Gup.norb
self.nbasis = self.Gup.nbasis + self.Gdn.nbasis
self.rho_up = np.zeros((self.norb, self.norb), dtype=float)
self.rho_dn = np.zeros((self.norb, self.norb), dtype=float)
self.JJ = defaultdict(lambda: 0.0j)
self.Jorb = defaultdict(lambda: 0.0j)
self.HR0_up = self.Gup.H0
self.HR0_dn = self.Gdn.H0
self.Delta = self.HR0_up - self.HR0_dn
if self.Gup.is_orthogonal and self.Gdn.is_orthogonal:
self.is_orthogonal = True
else:
self.is_orthogonal = False
#self.S0=self.Gup.S0
self._is_colinear = True
self.exchange_Jdict = {}
self.exchange_Jdict_orb = {}
self.biquadratic = False
def get_Delta(self, iatom):
orbs = self.iorb(iatom)
return self.Delta[np.ix_(orbs, orbs)]
def GR_atom(self, GR, iatom, jatom):
"""Given a green's function matrix, return the [iatom, jatom] component.
:param GR: Green's function matrix
:param iatom: index of atom i
:param jatom: index of atom j
:returns: G_ij
:rtype: complex matrix.
"""
orbi = self.iorb(iatom)
orbj = self.iorb(jatom)
return GR[np.ix_(orbi, orbj)]
def get_A_ijR(self, Gup, Gdn, iatom, jatom, de):
Rij_done = set()
for R, ijpairs in self.R_ijatom_dict.items():
if (iatom, jatom) in ijpairs and (R, iatom, jatom) not in Rij_done:
Gij_up = self.GR_atom(Gup[R], iatom, jatom)
Rm = tuple(-x for x in R)
Gji_dn = self.GR_atom(Gdn[Rm], jatom, iatom)
tmp = 0.0j
#t = self.get_Delta(iatom) @ Gij_up @ self.get_Delta(jatom) @ Gji_dn
t = np.einsum('ij, ji-> ij',
np.matmul(self.get_Delta(iatom), Gij_up),
np.matmul(self.get_Delta(jatom), Gji_dn))
if self.biquadratic:
A = np.einsum('ij, ji-> ij',
np.matmul(self.get_Delta(iatom), Gij_up),
np.matmul(self.get_Delta(jatom), Gji_up))
C = np.einsum('ij, ji-> ij',
np.matmul(self.get_Delta(iatom), Gij_down),
np.matmul(self.get_Delta(jatom), Gji_down))
tmp = np.sum(t)
self.Jorb[(R, iatom, jatom)] += t * de / (4.0 * np.pi)
self.JJ[(R, iatom, jatom)] += tmp * de / (4.0 * np.pi)
Rij_done.add((R, iatom, jatom))
if (Rm, jatom, iatom) not in Rij_done:
self.Jorb[(Rm, jatom, iatom)] += t * de / (4.0 * np.pi)
self.JJ[(Rm, jatom, iatom)] += tmp * de / (4.0 * np.pi)
Rij_done.add((Rm, jatom, iatom))
def get_all_A(self, Gup, Gdn, de):
"""
Calculate all A matrix elements
Loop over all magnetic atoms.
:param G: Green's function.
:param de: energy step.
"""
Rij_done = set()
for R, ijpairs in self.R_ijatom_dict.items():
for iatom, jatom in ijpairs:
if (R, iatom, jatom) not in Rij_done:
Rm = tuple(-x for x in R)
if (Rm, jatom, iatom) in Rij_done:
raise KeyError(
f"Strange (Rm, jatom, iatom) has already been calculated! {(Rm, jatom, iatom)}"
)
Gij_up = self.GR_atom(Gup[R], iatom, jatom)
Gji_dn = self.GR_atom(Gdn[Rm], jatom, iatom)
tmp = 0.0j
#t = self.get_Delta(iatom) @ Gij_up @ self.get_Delta(jatom) @ Gji_dn
t = np.einsum('ij, ji-> ij',
np.matmul(self.get_Delta(iatom), Gij_up),
np.matmul(self.get_Delta(jatom), Gji_dn))
tmp = np.sum(t)
self.Jorb[(R, iatom, jatom)] += t * de / (4.0 * np.pi)
self.JJ[(R, iatom, jatom)] += tmp * de / (4.0 * np.pi)
Rij_done.add((R, iatom, jatom))
if (Rm, jatom, iatom) not in Rij_done:
self.Jorb[(Rm, jatom, iatom)] += t * de / (4.0 * np.pi)
self.JJ[(Rm, jatom, iatom)] += tmp * de / (4.0 * np.pi)
Rij_done.add((Rm, jatom, iatom))
def A_to_Jtensor(self):
for key, val in self.JJ.items():
# key:(R, iatom, jatom)
R, iatom, jatom = key
ispin = self.ispin(iatom)
jspin = self.ispin(jatom)
keyspin = (R, ispin, jspin)
is_nonself = not (R == (0, 0, 0) and iatom == jatom)
Jij = np.imag(val) / np.sign(
np.dot(self.spinat[iatom], self.spinat[jatom]))
Jorbij = np.imag(self.Jorb[key]) / np.sign(
np.dot(self.spinat[iatom], self.spinat[jatom]))
if is_nonself:
self.exchange_Jdict[keyspin] = Jij
self.exchange_Jdict_orb[keyspin] = Jorbij
def get_rho_e(self, rho_up, rho_dn, de):
#GR0_up = GR_up[(0, 0, 0)]
#GR0_dn = GR_dn[(0, 0, 0)]
#if self.is_orthogonal:
# self.rho_up += -1.0 / np.pi * np.imag(GR0_up * de)
# self.rho_dn += -1.0 / np.pi * np.imag(GR0_dn * de)
#else:
# self.rho_up += -1.0 / np.pi * np.imag(self.S0@GR0_up * de)
# self.rho_dn += -1.0 / np.pi * np.imag(self.S0@GR0_dn * de)
self.rho_up += -1.0 / np.pi * np.imag(rho_up[(0, 0, 0)] * de)
self.rho_dn += -1.0 / np.pi * np.imag(rho_dn[(0, 0, 0)] * de)
def get_rho_atom(self):
"""
charges and spins from density matrices
"""
self.charges = np.zeros(len(self.atoms), dtype=float)
self.spinat = np.zeros((len(self.atoms), 3), dtype=float)
for iatom in self.orb_dict:
iorb = self.iorb(iatom)
tup = np.real(np.trace(self.rho_up[np.ix_(iorb, iorb)]))
tdn = np.real(np.trace(self.rho_dn[np.ix_(iorb, iorb)]))
# *2 because there is a 1/2 in the paui_block_all function
self.charges[iatom] = tup + tdn
self.spinat[iatom, 2] = tup - tdn
def finalize(self):
self.Gup.clean_cache()
self.Gdn.clean_cache()
path = 'TB2J_results/cache'
if os.path.exists(path):
shutil.rmtree(path)
def calculate_all(self):
"""
The top level.
"""
print("Green's function Calculation started.")
widgets = [
' [',
progressbar.Timer(),
'] ',
progressbar.Bar(),
' (',
progressbar.ETA(),
') ',
]
bar = progressbar.ProgressBar(maxval=self.contour.npoints,
widgets=widgets)
bar.start()
for ie in range(self.contour.npoints):
bar.update(ie)
e = self.contour.path[ie]
de = self.contour.de[ie]
GR_up, rho_up = self.Gup.get_GR(self.short_Rlist,
energy=e,
get_rho=True)
GR_dn, rho_dn = self.Gdn.get_GR(self.short_Rlist,
energy=e,
get_rho=True)
self.get_rho_e(rho_up, rho_dn, de)
self.get_all_A(GR_up, GR_dn, de)
self.get_rho_atom()
self.A_to_Jtensor()
bar.finish()
def write_output(self, path='TB2J_results'):
self._prepare_index_spin()
output = SpinIO(
atoms=self.atoms,
charges=self.charges,
spinat=self.spinat,
index_spin=self.index_spin,
colinear=True,
distance_dict=self.distance_dict,
exchange_Jdict=self.exchange_Jdict,
exchange_Jdict_orb=self.exchange_Jdict_orb,
dmi_ddict=None,
NJT_Jdict=None,
NJT_ddict=None,
Jani_dict=None,
biquadratic_Jdict=None,
description=self.description,
)
output.write_all()
class ExchangeNCL(Exchange):
"""
Non-collinear exchange
"""
def set_tbmodels(self, tbmodels):
"""
tbmodels should be in spinor form.
The basis should be orb1_up, orb2_up,...orbn_up, orb1_dn, orb2_dn....
"""
self.tbmodel = tbmodels
# TODO: check if tbmodels are really a tbmodel with SOC.
self.G = TBGreen(self.tbmodel,
self.kmesh,
self.efermi,
use_cache=self._use_cache,
nproc=self.np)
self.norb = self.G.norb
self.nbasis = self.G.nbasis
self.rho = np.zeros((self.nbasis, self.nbasis), dtype=complex)
self.A_ijR_list = defaultdict(lambda: [])
self.A_ijR = defaultdict(lambda: np.zeros((4, 4), dtype=complex))
self.HR0 = self.G.H0
self._is_collinear = False
self.Pdict = {}
def _prepare_NijR(self):
self.N = {}
for R in self.Rlist:
self.N[R] = np.zeros((self.nbasis, self.nbasis), dtype=complex)
def _prepare_Patom(self):
for iatom in self.ind_mag_atoms:
self.Pdict[iatom] = pauli_block_sigma_norm(self.get_H_atom(iatom))
def get_H_atom(self, iatom):
orbs = self.iorb(iatom)
return self.HR0[self.orb_slice[iatom], self.orb_slice[iatom]]
def get_P_iatom(self, iatom):
""" Calculate the norm of the Hamiltonian vector.
For each atom, the local hamiltonian of each orbital H(2*2 matrix)
can be written as H0* I + H1* sigma1 + H2*sigma2 + H3 *sigma3
where sigma is a Pauli matrix. return the norm of (H1, H2, H3) vector
:param iatom: index of atom
:returns: a matrix of norms P. P[i, j] is for orbital i and j.
:rtype: complex matrix of shape norb_i * norb_i.
"""
if self.Pdict == {}:
self._prepare_Patom()
return self.Pdict[iatom]
def GR_atom(self, GR, iatom, jatom):
"""Given a green's function matrix, return the [iatom, jatom] component.
:param GR: Green's function matrix
:param iatom: index of atom i
:param jatom: index of atom j
:returns: G_ij
:rtype: complex matrix.
"""
orbi = self.iorb(iatom)
orbj = self.iorb(jatom)
#return GR[np.ix_(orbi, orbj)]
return GR[self.orb_slice[iatom], self.orb_slice[jatom]]
def get_A_ijR(self, G, R, iatom, jatom):
""" calculate A from G for a energy slice (de).
It take the
.. math::
A^{uv} = p T^u p T^v dE / pi
where u, v are I, x, y, z (index 0, 1,2,3). p(i) = self.get_P_iatom(iatom)
T^u(ijR) (u=0,1,2,3) = pauli_block_all(G)
:param G: Green's function for all R, i, j.
:param iatom: i
:param jatom: j
:param de: energy step. used for integeration
:returns: a matrix of A_ij(u, v), where u, v =(0)0, x(1), y(2), z(3)
:rtype: 4*4 matrix
"""
GR = G[R]
Gij = self.GR_atom(GR, iatom, jatom)
Gij_Ixyz = pauli_block_all(Gij)
# G(j, i, -R)
Rm = tuple(-x for x in R)
GRm = G[Rm]
Gji = self.GR_atom(GRm, jatom, iatom)
Gji_Ixyz = pauli_block_all(Gji)
tmp = np.zeros((4, 4), dtype=complex)
for a in range(4):
pGp = self.get_P_iatom(iatom) @ Gij_Ixyz[a] @ self.get_P_iatom(
jatom)
for b in range(4):
AijRab = np.matmul(pGp, Gji_Ixyz[b])
tmp[a, b] = np.trace(AijRab)
return tmp / np.pi
def get_all_A(self, G):
"""
Calculate all A matrix elements
Loop over all magnetic atoms.
:param G: Green's function.
:param de: energy step.
"""
A_ijR_list = {}
for iR, R in enumerate(self.R_ijatom_dict):
for (iatom, jatom) in self.R_ijatom_dict[R]:
A = self.get_A_ijR(G, R, iatom, jatom)
A_ijR_list[(R, iatom, jatom)] = A
return A_ijR_list
def A_to_Jtensor(self):
"""
Calculate J tensors from A.
If we assume the exchange can be written as a bilinear tensor form,
J_{isotropic} = Tr Im (A^{00} - A^{xx} - A^{yy} - A^{zz})
J_{anisotropic}_uv = Tr Im (2A)
DMI = Tr Re (A^{0z} - A^{z0} )
"""
self.Jani = {}
self.DMI = {}
self.Jprime = {}
self.B = {}
self.exchange_Jdict = {}
self.debug_dict = {'DMI2': {}}
for key, val in self.A_ijR.items():
# key:(R, iatom, jatom)
R, iatom, jatom = key
Rm = tuple(-x for x in R)
valm = self.A_ijR[(Rm, jatom, iatom)]
ispin = self.ispin(iatom)
jspin = self.ispin(jatom)
keyspin = (R, ispin, jspin)
is_nonself = not (R == (0, 0, 0) and iatom == jatom)
Jiso = np.zeros((3, 3), dtype=float)
Ja = np.zeros((3, 3), dtype=float)
Dtmp = np.zeros(3, dtype=float)
Dtmp2 = np.zeros(3, dtype=float)
# Heisenberg like J.
for i in range(3):
Jiso[i, i] += np.imag(val[0, 0] - val[1, 1] - val[2, 2] -
val[3, 3])
if is_nonself:
self.exchange_Jdict[keyspin] = Jiso[0, 0]
# off-diagonal anisotropic exchange
for i in range(3):
for j in range(3):
Ja[i, j] = np.imag(val[i + 1, j + 1] + valm[i + 1, j + 1])
if is_nonself:
self.Jani[keyspin] = Ja
# DMI
for i in range(3):
Dtmp[i] = np.real(val[0, i + 1] - val[i + 1, 0])
# Dx = Jyz-Jzy
# Dy = Jzx-Jxz
# Dz = Jxy-Jyx
Dtmp2[0] = np.imag(val[2, 3] - val[3, 2])
Dtmp2[1] = np.imag(val[3, 1] - val[1, 3])
Dtmp2[2] = np.imag(val[1, 2] - val[2, 1])
if is_nonself:
self.DMI[keyspin] = Dtmp
self.debug_dict['DMI2'][keyspin] = Dtmp2
# isotropic exchange into bilinear and biqudratic parts:
# Jprime SiSj and B (SiSj)^2
if is_nonself:
Si = self.spinat[iatom]
Sj = self.spinat[jatom]
Jprime = np.imag(val[0, 0] - val[3, 3]) - 2 * np.sign(
np.dot(Si, Sj)) * np.imag(val[3, 3])
#Jprime = np.imag(val[0, 0] - 3*val[3, 3])
B = np.imag(val[3, 3])
self.B[keyspin] = Jprime, B
def get_N_e(self, GR, de):
"""
calcualte density matrix for all R,i, j
"""
self.N = defaultdict(lambda: 0.0)
for R, G in GR.items():
self.N[R] += -1.0 / np.pi * np.imag(G * de)
def get_rho_e(self, rhoR):
""" add component to density matrix from a green's function
:param GR: Green's funciton in real space.
"""
return -1.0 / np.pi * rhoR[0, 0, 0]
def get_total_charges(self):
return np.sum(np.imag(np.diag(self.rho)))
def get_rho_atom(self):
"""
calculate charge and spin for each atom.
"""
rho = {}
self.charges = np.zeros(len(self.atoms), dtype=float)
self.spinat = np.zeros((len(self.atoms), 3), dtype=float)
for iatom in self.orb_dict:
iorb = self.iorb(iatom)
tmp = self.rho[np.ix_(iorb, iorb)]
# *2 because there is a 1/2 in the paui_block_all function
rho[iatom] = np.array(
[np.trace(x) * 2 for x in pauli_block_all(tmp)])
self.charges[iatom] = np.imag(rho[iatom][0])
self.spinat[iatom, :] = np.imag(rho[iatom][1:])
self.rho_dict = rho
return self.rho_dict
def calculate_DMI_NJT(self):
"""
calculate exchange and DMI with the
D(i,j) =
"""
Ddict_NJT = {}
Jdict_NJT = {}
for R in self.short_Rlist:
N = self.N[tuple(-np.array(R))] # density matrix
t = self.tbmodel.get_hamR(R) # hopping parameter
for iatom in self.ind_mag_atoms:
orbi = self.iorb(iatom)
ni = len(orbi)
for jatom in self.ind_mag_atoms:
orbj = self.iorb(jatom)
nj = len(orbj)
Nji = N[np.ix_(orbj, orbi)]
tij = t[np.ix_(orbi, orbj)]
D = np.zeros(3, dtype=float)
J = np.zeros(3, dtype=float)
for dim in range(3):
#S_i = pauli_mat(ni, dim +
# 1) #*self.rho[np.ix_(orbi, orbi)]
#S_j = pauli_mat(nj, dim +
# 1) #*self.rho[np.ix_(orbj, orbj)]
# TODO: Note that rho is complex, not the imaginary part
S_i = pauli_mat(ni, dim + 1) * self.rho[np.ix_(
orbi, orbi)]
S_j = pauli_mat(nj, dim + 1) * self.rho[np.ix_(
orbj, orbj)]
# [S, t]+ = Si tij + tij Sj, where
# Si and Sj are the spin operator
# Here we do not have L operator, so J-> S
Jt = np.matmul(S_i, tij) + np.matmul(tij, S_j)
Jtminus = np.matmul(S_i, tij) - np.matmul(tij, S_j)
# D = -1/2 Tr Nji [J, tij]
# Trace over spin and orb
D[dim] = -0.5 * np.imag(np.trace(np.matmul(Nji, Jt)))
J[dim] = -0.5 * np.imag(
np.trace(np.matmul(Nji, Jtminus)))
ispin = self.ispin(iatom)
jspin = self.ispin(jatom)
Ddict_NJT[(R, ispin, jspin)] = D
Jdict_NJT[(R, ispin, jspin)] = J
self.Jdict_NJT = Jdict_NJT
self.Ddict_NJT = Ddict_NJT
return Ddict_NJT
def integrate(self, rhoRs, AijRs, method='simpson'):
"""
AijRs: a list of AijR,
wherer AijR: array of ((nR, n, n, 4,4), dtype=complex)
"""
if method == "trapezoidal":
integrate = trapezoidal_nonuniform
elif method == 'simpson':
integrate = simpson_nonuniform
self.rho = integrate(self.contour.path, rhoRs)
for iR, R in enumerate(self.R_ijatom_dict):
for (iatom, jatom) in self.R_ijatom_dict[R]:
f = AijRs[(R, iatom, jatom)]
self.A_ijR[(R, iatom, jatom)] = integrate(self.contour.path, f)
def get_AijR_rhoR(self, e):
GR, rhoR = self.G.get_GR(self.short_Rlist, energy=e, get_rho=True)
AijR = self.get_all_A(GR)
return AijR, self.get_rho_e(rhoR)
def save_AijR(self, AijRs, fname):
result = dict(path=self.contour.path, AijRs=AijRs)
with open(fname, 'wb') as myfile:
pickle.dump(result, myfile)
def calculate_all(self):
"""
The top level.
"""
print("Green's function Calculation started.")
widgets = [
' [',
progressbar.Timer(),
'] ',
progressbar.Bar(),
' (',
progressbar.ETA(),
') ',
]
bar = progressbar.ProgressBar(maxval=self.contour.npoints,
widgets=widgets)
bar.start()
rhoRs = []
GRs = []
AijRs = {}
if self.np > 1:
executor = ProcessPool(nodes=self.np)
results = executor.map(self.get_AijR_rhoR, self.contour.path)
else:
results = map(self.get_AijR_rhoR, self.contour.path)
for i, result in enumerate(results):
bar.update(i)
for iR, R in enumerate(self.R_ijatom_dict):
for (iatom, jatom) in self.R_ijatom_dict[R]:
if (R, iatom, jatom) in AijRs:
AijRs[(R, iatom, jatom)].append(result[0][R, iatom,
jatom])
else:
AijRs[(R, iatom, jatom)] = []
AijRs[(R, iatom, jatom)].append(result[0][R, iatom,
jatom])
rhoRs.append(result[1])
if self.np > 1:
executor.close()
executor.join()
executor.clear()
#self.save_AijRs(AijRs)
self.integrate(rhoRs, AijRs)
self.get_rho_atom()
self.A_to_Jtensor()
bar.finish()
def _prepare_index_spin(self):
# index_spin: index in spin hamiltonian of atom. starts from 1. -1 means not considered.
ind_matoms = []
self.index_spin = []
ispin = 0
for i, sym in enumerate(self.atoms.get_chemical_symbols()):
if sym in self.magnetic_elements:
ind_matoms.append(i)
self.index_spin.append(ispin)
ispin += 1
else:
self.index_spin.append(-1)
def write_output(self, path='TB2J_results'):
self._prepare_index_spin()
output = SpinIO(
atoms=self.atoms,
charges=self.charges,
spinat=self.spinat,
index_spin=self.index_spin,
colinear=False,
distance_dict=self.distance_dict,
exchange_Jdict=self.exchange_Jdict,
dmi_ddict=self.DMI,
NJT_Jdict=self.Jdict_NJT,
NJT_ddict=self.Ddict_NJT,
Jani_dict=self.Jani,
biquadratic_Jdict=self.B,
debug_dict=self.debug_dict,
description=self.description,
)
output.write_all(path=path)
def finalize(self):
self.G.clean_cache()
def run(self, path='TB2J_results'):
self.calculate_all()
self.write_output(path=path)
self.finalize()
class ExchangeCL2(ExchangeCL):
def set_tbmodels(self, tbmodels):
"""
only difference is a colinear tag.
"""
self.tbmodel_up, self.tbmodel_dn = tbmodels
self.Gup = TBGreen(self.tbmodel_up,
self.kmesh,
self.efermi,
use_cache=self._use_cache,
cache_path='TB2J_results/cache/spinup',
nproc=self.np)
self.Gdn = TBGreen(self.tbmodel_dn,
self.kmesh,
self.efermi,
use_cache=self._use_cache,
cache_path='TB2J_results/cache/spindn',
nproc=self.np)
self.norb = self.Gup.norb
self.nbasis = self.Gup.nbasis + self.Gdn.nbasis
self.rho_up_list = []
self.rho_dn_list = []
self.rho_up = np.zeros((self.norb, self.norb), dtype=float)
self.rho_dn = np.zeros((self.norb, self.norb), dtype=float)
self.Jorb_list = defaultdict(lambda: [])
self.JJ_list = defaultdict(lambda: [])
self.JJ = defaultdict(lambda: 0.0j)
self.Jorb = defaultdict(lambda: 0.0j)
self.HR0_up = self.Gup.H0
self.HR0_dn = self.Gdn.H0
self.Delta = self.HR0_up - self.HR0_dn
if self.Gup.is_orthogonal and self.Gdn.is_orthogonal:
self.is_orthogonal = True
else:
self.is_orthogonal = False
#self.S0=self.Gup.S0
self._is_colinear = True
self.exchange_Jdict = {}
self.exchange_Jdict_orb = {}
self.biquadratic = False
def _clean_tbmodels(self):
del self.tbmodel_up
del self.tbmodel_dn
del self.Gup.tbmodel
del self.Gdn.tbmodel
def _adjust_emin(self):
emin_up = self.Gup.find_energy_ingap(rbound=self.efermi -
5.0) - self.efermi
emin_dn = self.Gdn.find_energy_ingap(rbound=self.efermi -
5.0) - self.efermi
self.emin = min(emin_up, emin_dn)
print(f"A gap is found at {self.emin}, set emin to it.")
def get_Delta(self, iatom):
#orbs = self.iorb(iatom)
#return self.Delta[np.ix_(orbs, orbs)]
s = self.orb_slice[iatom]
return self.Delta[s, s]
def GR_atom(self, GR, iatom, jatom):
"""Given a green's function matrix, return the [iatom, jatom] component.
:param GR: Green's function matrix
:param iatom: index of atom i
:param jatom: index of atom j
:returns: G_ij
:rtype: complex matrix.
"""
#orbi = self.iorb(iatom)
#orbj = self.iorb(jatom)
#return GR[np.ix_(orbi, orbj)]
return GR[self.orb_slice[iatom], self.orb_slice[jatom]]
def get_A_ijR(self, Gup, Gdn, iatom, jatom):
Rij_done = set()
Jorb_list = dict()
JJ_list = dict()
for R, ijpairs in self.R_ijatom_dict.items():
if (iatom, jatom) in ijpairs and (R, iatom, jatom) not in Rij_done:
Gij_up = self.GR_atom(Gup[R], iatom, jatom)
Rm = tuple(-x for x in R)
Gji_dn = self.GR_atom(Gdn[Rm], jatom, iatom)
tmp = 0.0j
Deltai = self.get_Delta(iatom)
Deltaj = self.get_Delta(jatom)
t = np.einsum('ij, ji-> ij', np.matmul(Deltai, Gij_up),
np.matmul(Deltaj, Gji_dn))
if self.biquadratic:
A = np.einsum('ij, ji-> ij', np.matmul(Deltai, Gij_up),
np.matmul(Deltaj, Gji_up))
C = np.einsum('ij, ji-> ij', np.matmul(Deltai, Gij_down),
np.matmul(Deltaj, Gji_down))
tmp = np.sum(t)
self.Jorb_list[(R, iatom, jatom)].append(t / (4.0 * np.pi))
self.JJ_list[(R, iatom, jatom)].append(tmp / (4.0 * np.pi))
Rij_done.add((R, iatom, jatom))
if (Rm, jatom, iatom) not in Rij_done:
Jorb_list[(Rm, jatom, iatom)] = t / (4.0 * np.pi)
JJ_list[(Rm, jatom, iatom)] = tmp / (4.0 * np.pi)
Rij_done.add((Rm, jatom, iatom))
return Jorb_list, JJ_list
def get_all_A(self, Gup, Gdn):
"""
Calculate all A matrix elements
Loop over all magnetic atoms.
:param G: Green's function.
:param de: energy step.
"""
Rij_done = set()
Jorb_list = dict()
JJ_list = dict()
for R, ijpairs in self.R_ijatom_dict.items():
for iatom, jatom in ijpairs:
if (R, iatom, jatom) not in Rij_done:
Rm = tuple(-x for x in R)
if (Rm, jatom, iatom) in Rij_done:
raise KeyError(
f"Strange (Rm, jatom, iatom) has already been calculated! {(Rm, jatom, iatom)}"
)
Gij_up = self.GR_atom(Gup[R], iatom, jatom)
Gji_dn = self.GR_atom(Gdn[Rm], jatom, iatom)
tmp = 0.0j
#t = self.get_Delta(iatom) @ Gij_up @ self.get_Delta(jatom) @ Gji_dn
t = np.einsum('ij, ji-> ij',
np.matmul(self.get_Delta(iatom), Gij_up),
np.matmul(self.get_Delta(jatom), Gji_dn))
tmp = np.sum(t)
Jorb_list[(R, iatom, jatom)] = t / (4.0 * np.pi)
JJ_list[(R, iatom, jatom)] = tmp / (4.0 * np.pi)
Rij_done.add((R, iatom, jatom))
if (Rm, jatom, iatom) not in Rij_done:
Jorb_list[(Rm, jatom, iatom)] = t / (4.0 * np.pi)
JJ_list[(Rm, jatom, iatom)] = tmp / (4.0 * np.pi)
Rij_done.add((Rm, jatom, iatom))
return Jorb_list, JJ_list
def A_to_Jtensor(self):
for key, val in self.JJ.items():
# key:(R, iatom, jatom)
R, iatom, jatom = key
ispin = self.ispin(iatom)
jspin = self.ispin(jatom)
keyspin = (R, ispin, jspin)
is_nonself = not (R == (0, 0, 0) and iatom == jatom)
Jij = np.imag(val) / np.sign(
np.dot(self.spinat[iatom], self.spinat[jatom]))
Jorbij = np.imag(self.Jorb[key]) / np.sign(
np.dot(self.spinat[iatom], self.spinat[jatom]))
if is_nonself:
self.exchange_Jdict[keyspin] = Jij
self.exchange_Jdict_orb[keyspin] = Jorbij
def get_rho_e(self, rho_up, rho_dn):
#self.rho_up_list.append(-1.0 / np.pi * np.imag(rho_up[(0,0,0)]))
#self.rho_dn_list.append(-1.0 / np.pi * np.imag(rho_dn[(0,0,0)]))
rup = -1.0 / np.pi * rho_up[(0, 0, 0)]
rdn = -1.0 / np.pi * rho_dn[(0, 0, 0)]
return rup, rdn
def get_rho_atom(self):
"""
charges and spins from density matrices
"""
self.charges = np.zeros(len(self.atoms), dtype=float)
self.spinat = np.zeros((len(self.atoms), 3), dtype=float)
for iatom in self.orb_dict:
iorb = self.iorb(iatom)
tup = np.real(np.trace(self.rho_up[np.ix_(iorb, iorb)]))
tdn = np.real(np.trace(self.rho_dn[np.ix_(iorb, iorb)]))
self.charges[iatom] = tup + tdn
self.spinat[iatom, 2] = tup - tdn
def finalize(self):
self.Gup.clean_cache()
self.Gdn.clean_cache()
path = 'TB2J_results/cache'
if os.path.exists(path):
shutil.rmtree(path)
def integrate(self, method="simpson"):
if method == "trapezoidal":
integrate = trapezoidal_nonuniform
elif method == 'simpson':
integrate = simpson_nonuniform
self.rho_up = np.imag(integrate(self.contour.path, self.rho_up_list))
self.rho_dn = np.imag(integrate(self.contour.path, self.rho_dn_list))
for R, ijpairs in self.R_ijatom_dict.items():
for iatom, jatom in ijpairs:
self.Jorb[(R, iatom, jatom)] = integrate(
self.contour.path, self.Jorb_list[(R, iatom, jatom)])
self.JJ[(R, iatom,
jatom)] = integrate(self.contour.path,
self.JJ_list[(R, iatom, jatom)])
def get_AijR_rhoR(self, e):
GR_up, rho_up = self.Gup.get_GR(self.short_Rlist,
energy=e,
get_rho=True)
GR_dn, rho_dn = self.Gdn.get_GR(self.short_Rlist,
energy=e,
get_rho=True)
rup, rdn = self.get_rho_e(rho_up, rho_dn)
Jorb_list, JJ_list = self.get_all_A(GR_up, GR_dn)
return rup, rdn, Jorb_list, JJ_list
def calculate_all(self):
"""
The top level.
"""
print("Green's function Calculation started.")
widgets = [
' [',
progressbar.Timer(),
'] ',
progressbar.Bar(),
' (',
progressbar.ETA(),
') ',
]
bar = progressbar.ProgressBar(maxval=len(self.contour.path),
widgets=widgets)
bar.start()
if self.np == 1:
results = map(self.get_AijR_rhoR, self.contour.path)
else:
pool = ProcessPool(nodes=self.np)
results = pool.map(self.get_AijR_rhoR, self.contour.path)
for i, result in enumerate(results):
bar.update(i)
rup, rdn, Jorb_list, JJ_list = result
self.rho_up_list.append(rup)
self.rho_dn_list.append(rdn)
for iR, R in enumerate(self.R_ijatom_dict):
for (iatom, jatom) in self.R_ijatom_dict[R]:
key = (R, iatom, jatom)
self.Jorb_list[key].append(Jorb_list[key])
self.JJ_list[key].append(JJ_list[key])
if self.np > 1:
pool.close()
pool.join()
pool.clear()
self.integrate()
self.get_rho_atom()
self.A_to_Jtensor()
bar.finish()
def write_output(self, path='TB2J_results'):
self._prepare_index_spin()
output = SpinIO(
atoms=self.atoms,
charges=self.charges,
spinat=self.spinat,
index_spin=self.index_spin,
colinear=True,
distance_dict=self.distance_dict,
exchange_Jdict=self.exchange_Jdict,
exchange_Jdict_orb=self.exchange_Jdict_orb,
dmi_ddict=None,
NJT_Jdict=None,
NJT_ddict=None,
Jani_dict=None,
biquadratic_Jdict=None,
description=self.description,
)
output.write_all(path=path)