def diagonalize(ten_dq, umat):
emat = edrixs.cb_op(edrixs.cf_cubic_d(ten_dq),
edrixs.tmat_c2r('d', ispin=True))
H = (edrixs.build_opers(4, umat, basis) +
edrixs.build_opers(2, emat, basis))
e, v = scipy.linalg.eigh(H)
return e - e.min()
orbital_energies = np.array([e for orbital_energy in
[+0.6 * ten_dq, # dz2
-0.4 * ten_dq, # dzx
-0.4 * ten_dq, # dzy
+0.6 * ten_dq, # dx2-y2
-0.4 * ten_dq] # dxy)
for e in [orbital_energy]*2])
CF[diagonal_indices, diagonal_indices] = orbital_energies
################################################################################
# The valence band SOC is constructed in the normal way and transformed into the
# real harmonic basis.
soc = edrixs.cb_op(edrixs.atom_hsoc('d', zeta_d_i), edrixs.tmat_c2r('d', True))
################################################################################
# The total impurity matrices for the ground and core-hole states are then
# the sum of crystal field and spin-orbit coupling. We further needed to apply
# an energy shift along the matrix diagonal, which we do using the
# :code:`np.eye` function which creates a diagonal matrix of ones.
E_d_mat = E_d*np.eye(norb_d)
E_dc_mat = E_dc*np.eye(norb_d)
imp_mat = CF + soc + E_d_mat
imp_mat_n = CF + soc + E_dc_mat
################################################################################
# The energy level of the bath(s) is described by a matrix where the row index
# denotes which bath and the column index denotes which orbital. Here we have
# only one bath, with 10 spin-orbitals. We initialize the matrix to
def get_hopping_coulomb(locaxis):
# Number of orbitals
nt2g, nporb, norbs = 6, 6, 24
# On-site Coulomb interaction tensor
Ud, JH = edrixs.UJ_to_UdJH(2, 0.3)
F0_d, F2_d, F4_d = edrixs.UdJH_to_F0F2F4(Ud, JH)
G1_dp, G3_dp = 0.957, 0.569
F0_dp, F2_dp = edrixs.get_F0('dp', G1_dp, G3_dp), 1.107
umat_t2g_i = edrixs.get_umat_slater('t2g', F0_d, F2_d, F4_d)
params = [
F0_d,
F2_d,
F4_d, # Fk for d
F0_dp,
F2_dp, # Fk for dp
G1_dp,
G3_dp, # Gk for dp
0.0,
0.0 # Fk for p
]
umat_t2gp_n = edrixs.get_umat_slater('t2gp', *params)
# static core-hole potential
static_v = 2.0
for i in range(0, nt2g):
for j in range(nt2g, nt2g + nporb):
umat_t2gp_n[i, j, j, i] += static_v
umat_i = np.zeros((norbs, norbs, norbs, norbs), dtype=np.complex128)
umat_n = np.zeros((norbs, norbs, norbs, norbs), dtype=np.complex128)
umat_i[0:6, 0:6, 0:6, 0:6] = umat_t2g_i
umat_i[6:12, 6:12, 6:12, 6:12] = umat_t2g_i
indx = np.array([[0, 1, 2, 3, 4, 5, 12, 13, 14, 15, 16, 17],
[6, 7, 8, 9, 10, 11, 18, 19, 20, 21, 22, 23]])
for m in range(2):
for i in range(12):
for j in range(12):
for k in range(12):
for l in range(12):
umat_n[indx[m, i], indx[m, j], indx[m, k],
indx[m, l]] += umat_t2gp_n[i, j, k, l]
emat_i = np.zeros((norbs, norbs), dtype=np.complex128)
emat_n = np.zeros((norbs, norbs), dtype=np.complex128)
# SOC
zeta_d_i, zeta_p_n = 0.35, 1072.6666666666667
soc_d = edrixs.atom_hsoc('t2g', zeta_d_i)
soc_p = edrixs.atom_hsoc('p', zeta_p_n)
emat_i[0:6, 0:6] += soc_d
emat_i[6:12, 6:12] += soc_d
emat_n[0:6, 0:6] += soc_d
emat_n[6:12, 6:12] += soc_d
emat_n[12:18, 12:18] += soc_p
emat_n[18:24, 18:24] += soc_p
for i in range(2 * nt2g):
emat_n[i, i] -= 6 * static_v
# Crystal field and hoppings between the two Ir-sites
t1, t2, delta = -0.18, 0.036, -0.03
# Uncomment the following line to do calculation without hopping and crystal filed splitting.
# t1, t2, delta = 0, 0, -0.03
crys_tmp = np.array(
[[0, delta, delta, t1, t2, t1], [delta, 0, delta, t2, t1, t1],
[delta, delta, 0, t1, t1, t2], [t1, t2, t1, 0, delta, delta],
[t2, t1, t1, delta, 0, delta], [t1, t1, t2, delta, delta, 0]],
dtype=np.complex)
# transform spin to local axis
dmat = np.zeros((2, 2, 2), dtype=np.complex128)
ang1, ang2, ang3 = edrixs.rmat_to_euler(locaxis[0])
dmat[0] = edrixs.dmat_spinor(ang1, ang2, ang3)
ang1, ang2, ang3 = edrixs.rmat_to_euler(locaxis[1])
dmat[1] = edrixs.dmat_spinor(ang1, ang2, ang3)
t_spinor = np.zeros((12, 12), dtype=np.complex128)
for i in range(2):
off = i * 6
t_spinor[off + 0:off + 2, off + 0:off + 2] = dmat[i]
t_spinor[off + 2:off + 4, off + 2:off + 4] = dmat[i]
t_spinor[off + 4:off + 6, off + 4:off + 6] = dmat[i]
crys_spin = np.zeros((12, 12), dtype=np.complex128)
crys_spin[0:12:2, 0:12:2] = crys_tmp
crys_spin[1:12:2, 1:12:2] = crys_tmp
t_orb = np.zeros((12, 12), dtype=np.complex128)
t_orb[0:6, 0:6] = edrixs.tmat_r2c('t2g', True)
t_orb[6:12, 6:12] = edrixs.tmat_r2c('t2g', True)
crys_spin[:, :] = edrixs.cb_op(crys_spin, np.dot(t_spinor, t_orb))
emat_i[0:12, 0:12] += crys_spin
emat_n[0:12, 0:12] += crys_spin
# Write to files
# ED inputs
edrixs.write_emat(emat_i, "ed/hopping_i.in")
edrixs.write_umat(umat_i, "ed/coulomb_i.in")
# XAS inputs
edrixs.write_emat(emat_n, "xas/hopping_n.in")
edrixs.write_umat(umat_n, "xas/coulomb_n.in")
# RIXS inputs
edrixs.write_emat(emat_i, "rixs_pp/hopping_i.in")
edrixs.write_umat(umat_i, "rixs_pp/coulomb_i.in")
edrixs.write_emat(emat_n, "rixs_pp/hopping_n.in")
edrixs.write_umat(umat_n, "rixs_pp/coulomb_n.in")
edrixs.write_emat(emat_i, "rixs_ps/hopping_i.in")
edrixs.write_umat(umat_i, "rixs_ps/coulomb_i.in")
edrixs.write_emat(emat_n, "rixs_ps/hopping_n.in")
edrixs.write_umat(umat_n, "rixs_ps/coulomb_n.in")
# t2g orbitals, dxz, dyz, dxy, :math:`\\hat{d}^{\\dagger}_{\\alpha}\\hat{d}_{\\alpha}`
# First, write their matrice in the real harmonics basis
# |dxz,up>, |dxz,dn>, |dyz,up>, |dyz,dn>, |dxy,up>, |dxy,dn>
# In this basis, they take simple form, only the diagonal terms have element 1
nd_oper = np.zeros((norb, norb, norb), dtype=np.complex)
nd_oper[0, 0, 0] = 1
nd_oper[1, 1, 1] = 1
nd_oper[2, 2, 2] = 1
nd_oper[3, 3, 3] = 1
nd_oper[4, 4, 4] = 1
nd_oper[5, 5, 5] = 1
# Then transform to the complex harmonics basis
# |-1,up>, |-1,dn>, |0,up>, |0,dn>, |+1,up>, |+1,dn>
# comment the following line to calculate the occupancy number
# of the complex harmonics orbitals
nd_oper = edrixs.cb_op(nd_oper, edrixs.tmat_r2c('t2g', True))
# Build the many-body operators for nd
nd_manybody_oper = edrixs.build_opers(2, nd_oper, basis)
# Build many-body Hamiltonian for four-fermion terms in the Fock basis
# H has the dimension of 15*15
H_U = edrixs.build_opers(4, umat, basis)
# Build many-body Hamiltonian for two-fermion terms in the Fock basis
H_soc = edrixs.build_opers(2, emat_soc, basis)
H_zeeman = edrixs.build_opers(2, emat_zeeman, basis)
# The scipy diagonalization returns eigenvalues in ascending order, each repeated according
# to its multiplicity. eigenvectors are returned as a set of column vectors.
# eigenvalue eigenval[n] is associated with eignevector eigenvec[:, n]
# case 1: without SOC
H = H_U + H_zeeman
# applied to the off-diagonal terms of :code:`emat`.
indx1 = np.arange(norb_d)
indx2 = np.arange(norb_d, norb_d * 2)
emat_rhb[indx1, indx2] += hyb[0]
emat_rhb[indx2, indx1] += np.conj(hyb[0])
################################################################################
# We now need to transform into the complex harmonic basis. We assign
# the two diagonal blocks of a :math:`20\times20` matrix to the
# conjugate transpose of the transition matrix.
tmat = np.eye(ntot, dtype=complex)
for i in range(2):
off = i * norb_d
tmat[off:off + norb_d, off:off + norb_d] = np.conj(np.transpose(trans_c2n))
emat_chb = edrixs.cb_op(emat_rhb, tmat)
################################################################################
# The spin exchange is built from the spin operators and the effective field
# is applied to the :math:`d`-shell region of the matrix.
v_orbl = 2
sx = edrixs.get_sx(v_orbl)
sy = edrixs.get_sy(v_orbl)
sz = edrixs.get_sz(v_orbl)
zeeman = ext_B[0] * (2 * sx) + ext_B[1] * (2 * sy) + ext_B[2] * (2 * sz)
emat_chb[0:norb_d, 0:norb_d] += zeeman
################################################################################
# Build the Fock basis and Hamiltonain and Diagonalize
# ------------------------------------------------------------------------------
# We create the fock basis and build the Hamiltonian using the full set of
# these operators i.e.
#
# .. math::
# \mathbf{S}^2 = S^2_x + S^2_y + S^2_z\\
# \mathbf{L}^2 = L^2_x + L^2_y + L^2_z\\
# \mathbf{J}^2 = J^2_x + J^2_y + J^2_z
#
L2 = np.dot(opL[0], opL[0]) + np.dot(opL[1], opL[1]) + np.dot(opL[2], opL[2])
S2 = np.dot(opS[0], opS[0]) + np.dot(opS[1], opS[1]) + np.dot(opS[2], opS[2])
J2 = np.dot(opJ[0], opJ[0]) + np.dot(opJ[1], opJ[1]) + np.dot(opJ[2], opJ[2])
################################################################################
# Remember that the eigenvalues of :math:`\mathbf{S}^2` are in the form
# :math:`S(S+1)` etc. and that they can be obtained by calculating the
# projection of the operators onto our eigenvectors.
L2_val = edrixs.cb_op(L2, v).diagonal().real
S2_val = edrixs.cb_op(S2, v).diagonal().real
J2_val = edrixs.cb_op(J2, v).diagonal().real
################################################################################
# We can determine the degeneracy of the eigenvalues numerically and print out
# the values as follows
e = np.round(e, decimals=6)
degeneracy = [sum(eval == e) for eval in e]
header = "{:<3s}\t{:>8s}\t{:>8s}\t{:>8s}\t{:>8s}"
print(header.format("# ", "E ", "S(S+1)", "L(L+1)", "Degen."))
for i, eigenvalue in enumerate(e):
values_list = [i, eigenvalue, S2_val[i], L2_val[i], degeneracy[i]]
print("{:<3d}\t{:8.3f}\t{:8.3f}\t{:8.3f}\t{:>3d}".format(*values_list))
################################################################################
# We see :math:`S=0` and :math:`S=1` states coming from the
def ed():
# 1-10: Ni-3d valence orbitals, 11-16: Ni-2p core orbitals
# Single particle basis: complex shperical Harmonics
ndorb, nporb, ntot = 10, 6, 16
emat_i = np.zeros((ntot, ntot), dtype=np.complex)
emat_n = np.zeros((ntot, ntot), dtype=np.complex)
# 4-index Coulomb interaction tensor, parameterized by
# Slater integrals, which are obtained from Cowan's code
F2_d, F4_d = 7.9521, 4.9387
# Averaged dd Coulomb interaction is set to be zero
F0_d = edrixs.get_F0('d', F2_d, F4_d)
G1_dp, G3_dp = 4.0509, 2.3037
# Averaged dp Coulomb interaction is set to be zero
F0_dp, F2_dp = edrixs.get_F0('dp', G1_dp, G3_dp), 7.33495
umat_i = edrixs.get_umat_slater(
'dp',
F0_d,
F2_d,
F4_d, # dd
0,
0,
0,
0, # dp
0,
0) # pp
umat_n = edrixs.get_umat_slater(
'dp',
F0_d,
F2_d,
F4_d, # dd
F0_dp,
F2_dp,
G1_dp,
G3_dp, # dp
0,
0) # pp
# Atomic spin-orbit coupling
zeta_d, zeta_p = 0.083, 11.24
emat_i[0:ndorb, 0:ndorb] += edrixs.atom_hsoc('d', zeta_d)
emat_n[0:ndorb, 0:ndorb] += edrixs.atom_hsoc('d', zeta_d)
emat_n[ndorb:ntot, ndorb:ntot] += edrixs.atom_hsoc('p', zeta_p)
# Tetragonal crystal field splitting terms,
# which are first defined in the real cubic Harmonics basis,
# and then transformed to complex shperical Harmonics basis.
dt, ds, dq = 0.011428, 0.035714, 0.13
tmp = np.zeros((5, 5), dtype=np.complex)
tmp[0, 0] = 6 * dq - 2 * ds - 6 * dt # d3z2-r2
tmp[1, 1] = -4 * dq - 1 * ds + 4 * dt # dzx
tmp[2, 2] = -4 * dq - 1 * ds + 4 * dt # dzy
tmp[3, 3] = 6 * dq + 2 * ds - 1 * dt # dx2-y2
tmp[4, 4] = -4 * dq + 2 * ds - 1 * dt # dxy
tmp[:, :] = edrixs.cb_op(tmp, edrixs.tmat_r2c('d'))
emat_i[0:ndorb:2, 0:ndorb:2] += tmp
emat_i[1:ndorb:2, 1:ndorb:2] += tmp
emat_n[0:ndorb:2, 0:ndorb:2] += tmp
emat_n[1:ndorb:2, 1:ndorb:2] += tmp
# Build Fock basis in its binary form
basis_i = edrixs.get_fock_bin_by_N(ndorb, 8, nporb, nporb)
basis_n = edrixs.get_fock_bin_by_N(ndorb, 9, nporb, nporb - 1)
ncfg_i, ncfg_n = len(basis_i), len(basis_n)
# Build many-body Hamiltonian in Fock basis
hmat_i = np.zeros((ncfg_i, ncfg_i), dtype=np.complex)
hmat_n = np.zeros((ncfg_n, ncfg_n), dtype=np.complex)
hmat_i[:, :] += edrixs.two_fermion(emat_i, basis_i, basis_i)
hmat_i[:, :] += edrixs.four_fermion(umat_i, basis_i)
hmat_n[:, :] += edrixs.two_fermion(emat_n, basis_n, basis_n)
hmat_n[:, :] += edrixs.four_fermion(umat_n, basis_n)
# Do exact-diagonalization to get eigenvalues and eigenvectors
eval_i, evec_i = np.linalg.eigh(hmat_i)
eval_n, evec_n = np.linalg.eigh(hmat_n)
# Build dipolar transition operators
dipole = np.zeros((3, ntot, ntot), dtype=np.complex)
T_abs = np.zeros((3, ncfg_n, ncfg_i), dtype=np.complex)
T_emi = np.zeros((3, ncfg_i, ncfg_n), dtype=np.complex)
tmp = edrixs.get_trans_oper('dp')
for i in range(3):
dipole[i, 0:ndorb, ndorb:ntot] = tmp[i]
# First, in the Fock basis
T_abs[i] = edrixs.two_fermion(dipole[i], basis_n, basis_i)
# Then, transfrom to the eigenvector basis
T_abs[i] = edrixs.cb_op2(T_abs[i], evec_n, evec_i)
T_emi[i] = np.conj(np.transpose(T_abs[i]))
return eval_i, eval_n, T_abs, T_emi
print(v[:, 6:].real)
################################################################################
# These are the set of so-called :math:`e_{g}` orbitals, composed of
# :math:`Y^2_2, Y^{-2}_2, Y^{0}_2`. We can use edrixs to prove that
# :code:`cfmat` would be diagonal in the real
# harmonic basis. An operator :math:`\hat{O}` can be transformed into an
# operator in another basis :math:`\hat{O}^{\prime}` using a unitary
# transformation matrix :math:`T` as
#
# .. math::
#
# \hat{O}^{\prime} = (T)^{\dagger} \hat{O} (T).
#
# This is computed as follows
cfmat_rhb = edrixs.cb_op(cfmat, edrixs.tmat_c2r('d', ispin=True))
print(cfmat_rhb.real)
################################################################################
# where :code:`edrixs.tmat_c2r('d', ispin=True)` is the transformation matrix.
# We needed to tell edrixs that we are working with a :math:`d`-shell and that it
# should include spin. We could also have transformed :code:`v` to see how these
# eignevectors are composed of the real harmonic basis. We will see an example
# of this later.
################################################################################
# Crystal field on an atom
# ------------------------------------------------------------------------------
# To simulate the solid state, we need to combine the crystal field with Coulomb
# interactions. Let us choose an atomic model for Ni.
l = 2
indx = np.array([[0, 1, 2, 3, 4, 5, 12, 13, 14, 15, 16, 17],
[6, 7, 8, 9, 10, 11, 18, 19, 20, 21, 22, 23]])
for m in range(2):
for i in range(12):
for j in range(12):
for k in range(12):
for l in range(12):
umat_n[m, indx[m, i], indx[m, j], indx[m, k],
indx[m, l]] += umat_t2gp_n[i, j, k, l]
emat_i = np.zeros((norbs, norbs), dtype=np.complex128)
emat_n = np.zeros((2, norbs, norbs), dtype=np.complex128)
soc_d = edrixs.cb_op(edrixs.atom_hsoc('t2g', zeta_d_i),
edrixs.tmat_c2r('t2g', True))
soc_p = edrixs.cb_op(edrixs.atom_hsoc('p', zeta_p_n),
edrixs.tmat_c2r('p', True))
emat_i[0:6, 0:6] += soc_d
emat_i[6:12, 6:12] += soc_d
emat_n[0, 0:6, 0:6] += soc_d
emat_n[0, 6:12, 6:12] += soc_d
emat_n[0, 12:18, 12:18] += soc_p
emat_n[1, 0:6, 0:6] += soc_d
emat_n[1, 6:12, 6:12] += soc_d
emat_n[1, 18:24, 18:24] += soc_p
# crystal field and hopping between the two Ir atom
a, b, c = -0.18, 0.036, -0.03
# a, b, c = -0.0, 0.00, -0.00
spin_mom = np.zeros((3, norb, norb), dtype=np.complex128)
spin_mom[:, :2, :2] = spin_mom[:, 2:, 2:] = spin_mom_one_site
opS = edrixs.build_opers(2, spin_mom, basis)
opS_squared = (np.dot(opS[0], opS[0]) + np.dot(opS[1], opS[1])
+ np.dot(opS[2], opS[2]))
################################################################################
# This time let us include a tiny magnetic field along the :math:`z`-axis, so
# that we have a well-defined measurement axis and print out the expectation
# values.
zeeman = np.zeros((norb, norb), dtype=np.complex128)
zeeman[:2, :2] = zeeman[2:, 2:] = 1e-8*spin_mom_one_site[2]
e, v = diagonalize(1000, 1, extra_emat=zeeman)
Ssq_exp = edrixs.cb_op(opS_squared, v).diagonal().real
Sz_exp = edrixs.cb_op(opS[2], v).diagonal().real
header = "{:<10s}\t{:<6s}\t{:<6s}"
print(header.format("E", "S(S+1)", "<Sz>"))
for i in range(len(e)):
print("{:<2f}\t{:.1f}\t{:.1f}".format(e[i], Ssq_exp[i], Sz_exp[i]))
################################################################################
# For :math:`U \gg t` the two states with double occupancy acquire an energy of
# approximately :math:`U`. The low energy states are a :math:`S=0` singlet and
# and :math:`S=1` triplet, which are split by :math:`4t^2/U`, which is the
# magnetic exchange term.
################################################################################
# :math:`U` dependence
def get_hopping_coulomb(locaxis):
# Number of orbitals for each site
ndorb, nporb = 6, 4
# Number of sites
nsite = 2
# Total number of orbitals
ntot = nsite * (ndorb + nporb)
# orbital orders:
# 0-5: 1st-site-t2g
# 6-11: 2nd-site-t2g
# 12-15: 1st-site-2p
# 16-19: 2nd-site-2p
# On-site Coulomb interaction tensor
U, J = 2.0, 0.3
Ud, JH = edrixs.UJ_to_UdJH(U, J)
F0_dd, F2_dd, F4_dd = edrixs.UdJH_to_F0F2F4(Ud, JH) # k=0, 2, 2*l
G1_dp, G3_dp = 0.957, 0.569 # k=|2-1|, |2+1|
F0_dp, F2_dp = edrixs.get_F0('dp', G1_dp,
G3_dp), 1.107 # k=0, min(2*2, 2*1)
# just one site t2g-subspace
umat_tmp_i = edrixs.get_umat_slater('t2g', F0_dd, F2_dd, F4_dd)
params = [
F0_dd,
F2_dd,
F4_dd, # FX for dd
F0_dp,
F2_dp, # FX for dp
G1_dp,
G3_dp, # GX for dp
0,
0 # FX for pp
]
# just one site
umat_tmp_n = edrixs.get_umat_slater('t2gp32', *params) # 2p_3/2 -> t2g
# static core-hole potential
static_v = 2.0
for i in range(0, ndorb):
for j in range(ndorb, ndorb + nporb):
umat_tmp_n[i, j, j, i] += static_v
# two sites as a whole
umat_i = np.zeros((ntot, ntot, ntot, ntot), dtype=np.complex)
umat_n = np.zeros((ntot, ntot, ntot, ntot), dtype=np.complex)
umat_i[0:ndorb, 0:ndorb, 0:ndorb,
0:ndorb] = umat_tmp_i # 1st site 5d-valence
umat_i[ndorb:2 * ndorb, ndorb:2 * ndorb, ndorb:2 * ndorb,
ndorb:2 * ndorb] = umat_tmp_i # 2nd site 5d-valence
indx = np.array([
[
0,
1,
2,
3,
4,
5, # orbital indices for 1st site 5d-t2g
12,
13,
14,
15
], # orbital indices for 1st site 2p-core
[
6,
7,
8,
9,
10,
11, # orbital indices for 2nd site 5d-t2g
16,
17,
18,
19
] # orbital indices for 2nd site 2p-core
])
# copy umat_tmp_n (one site) to umat_n (two sites)
ndp = ndorb + nporb
for m in range(nsite):
for i in range(ndp):
for j in range(ndp):
for k in range(ndp):
for l in range(ndp):
umat_n[indx[m, i], indx[m, j], indx[m, k],
indx[m, l]] += umat_tmp_n[i, j, k, l]
# two fermion terms, SOC, crystal field, and hopping between the two sites
emat_i = np.zeros((ntot, ntot), dtype=np.complex)
emat_n = np.zeros((ntot, ntot), dtype=np.complex)
# SOC
zeta_d_i = 0.35
soc_d = edrixs.atom_hsoc('t2g', zeta_d_i)
emat_i[0:ndorb, 0:ndorb] += soc_d
emat_i[ndorb:2 * ndorb, ndorb:2 * ndorb] += soc_d
emat_n[0:ndorb, 0:ndorb] += soc_d
emat_n[ndorb:2 * ndorb, ndorb:2 * ndorb] += soc_d
# Terms from static core-hole potential
for i in range(2 * ndorb):
emat_n[i, i] -= nporb * static_v
# Crystal field and hoppings between the two Ir-sites
d = -0.03 # trgional splitting in t2g-subspace
# Uncomment the following line to do calculation without hopping and crystal filed splitting.
t1, t2 = -0.18, 0.036 # hopping between the two-sites in t2g-subspace
cf_tmp = np.array([ # dzx_1, dzy_1, dxy_1, dzx_2, dzy_2, dxy_2
[0, d, d, t1, t2, t1], # dzx_1
[d, 0, d, t2, t1, t1], # dzy_1
[d, d, 0, t1, t1, t2], # dxy_1
[t1, t2, t1, 0, d, d], # dzx_2
[t2, t1, t1, d, 0, d], # dzy_2
[t1, t1, t2, d, d, 0], # dxy_2
])
# Including spin degree of freedom, in global axis
cf_spin = np.zeros((2 * ndorb, 2 * ndorb), dtype=np.complex)
cf_spin[0:2 * ndorb:2, 0:2 * ndorb:2] = cf_tmp
cf_spin[1:2 * ndorb:2, 1:2 * ndorb:2] = cf_tmp
# Transform spin basis to local axis
# 1/2-spinor matrix
t_spinor = np.zeros((2 * ndorb, 2 * ndorb), dtype=np.complex128)
for i in range(nsite):
alpha, beta, gamma = edrixs.rmat_to_euler(locaxis[i])
dmat = edrixs.dmat_spinor(alpha, beta, gamma)
for j in range(ndorb // 2):
off = i * ndorb + j * 2
t_spinor[off:off + 2, off:off + 2] = dmat
# Transform orbital basis from real cubic to complex harmonics
t_orb = np.zeros((2 * ndorb, 2 * ndorb), dtype=np.complex128)
t_orb[0:ndorb, 0:ndorb] = edrixs.tmat_r2c('t2g', True)
t_orb[ndorb:2 * ndorb, ndorb:2 * ndorb] = edrixs.tmat_r2c('t2g', True)
# Do the tranformation
cf_spin[:, :] = edrixs.cb_op(cf_spin, np.dot(t_spinor, t_orb))
emat_i[0:2 * ndorb, 0:2 * ndorb] += cf_spin
emat_n[0:2 * ndorb, 0:2 * ndorb] += cf_spin
# Write emat and umat to files
# ED inputs
edrixs.write_emat(emat_i, "ed/hopping_i.in")
edrixs.write_umat(umat_i, "ed/coulomb_i.in")
# XAS inputs
edrixs.write_emat(emat_n, "xas/hopping_n.in")
edrixs.write_umat(umat_n, "xas/coulomb_n.in")
# RIXS inputs
edrixs.write_emat(emat_i, "rixs_pp/hopping_i.in")
edrixs.write_umat(umat_i, "rixs_pp/coulomb_i.in")
edrixs.write_emat(emat_n, "rixs_pp/hopping_n.in")
edrixs.write_umat(umat_n, "rixs_pp/coulomb_n.in")
edrixs.write_emat(emat_i, "rixs_ps/hopping_i.in")
edrixs.write_umat(umat_i, "rixs_ps/coulomb_i.in")
edrixs.write_emat(emat_n, "rixs_ps/hopping_n.in")
edrixs.write_umat(umat_n, "rixs_ps/coulomb_n.in")