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
dmu = 0.0
m1, m2 = dmu / 2.0, -dmu / 2.0
crys_tmp = np.array(
[[m1, c, c, a, b, a], [c, m1, c, b, a, a], [c, c, m1, a, a, b],
[a, b, a, m2, c, c], [b, a, a, c, m2, c], [a, a, b, c, c, m2]],
dtype=np.complex128)
# transform spin to local axis
dmat = np.zeros((2, 2, 2), dtype=np.complex128)
ang1, ang2, ang3 = edrixs.rmat_to_euler(np.transpose(Ir_loc2g[0]))
dmat[0] = edrixs.dmat_spinor(ang1, ang2, ang3)
ang1, ang2, ang3 = edrixs.rmat_to_euler(np.transpose(Ir_loc2g[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
crys_spin[:, :] = edrixs.cb_op(crys_spin, t_spinor)
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")
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")