def get_hopping_coulomb():
N_site = 16
norbs = 32
U, t = 4.0, -1.0
umat = np.zeros((norbs, norbs, norbs, norbs), dtype=np.complex128)
for i in range(N_site):
off = i * 2
umat[off, off + 1, off + 1, off] = U
hopp = np.zeros((N_site, N_site), dtype=np.complex128)
indx = [[3, 1, 12, 4], [0, 2, 13, 5], [1, 3, 14, 6], [2, 0, 15, 7],
[7, 5, 0, 8], [4, 6, 1, 9], [5, 7, 2, 10], [6, 4, 3, 11],
[11, 9, 4, 12], [8, 10, 5, 13], [9, 11, 6, 14], [10, 8, 7, 15],
[15, 13, 8, 0], [
12,
14,
9,
1,
], [13, 15, 10, 2], [14, 12, 11, 3]]
for i, item in enumerate(indx):
hopp[i, item[0]] = hopp[i, item[1]] = hopp[i,
item[2]] = hopp[i,
item[3]] = t
hopping = np.zeros((norbs, norbs), dtype=np.complex128)
hopping[0:norbs:2, 0:norbs:2] = hopp
hopping[1:norbs:2, 1:norbs:2] = hopp
edrixs.write_emat(hopping, "hopping_i.in", 1E-10)
edrixs.write_umat(umat, "coulomb_i.in", 1E-10)
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")
# SOC strength
zeta_f_i = 0.261 * 0.9
hsoc_i = edrixs.atom_hsoc('f', zeta_f_i)
# prepare files for ed.x
# write control parameters to file
edrixs.write_config(ed_solver=2,
num_val_orbs=norbs,
neval=100,
ncv=200,
nvector=1,
idump=True)
# write nonzeros terms of two-fermion terms hsoc_i to file 'hopping_i.in', read by ed.x
edrixs.write_emat(hsoc_i, 'hopping_i.in', 1E-10)
# write nonzeros terms of four-fermion terms umat to file 'coulomb_i.in', read by ed.x
edrixs.write_umat(umat_i, 'coulomb_i.in', 1E-10)
# write fock basis of decimal format to file 'fock_i.in', read by ed.x
edrixs.write_fock_dec_by_N(norbs, noccu, "fock_i.in")
# we also use pure Python ED solver to get the eigenvalues
print("edrixs >>> building Fock basis ...")
basis_i = edrixs.get_fock_bin_by_N(norbs, noccu)
print("edrixs >>> Done!")
print("edrixs >>> building Hamiltonian ...")
H = edrixs.build_opers(2, hsoc_i, basis_i)
H += edrixs.build_opers(4, umat_i, basis_i)
print("edrixs >>> Done!")
print("edrixs >>> diagonalize Hamiltonian ...")
eval_i, evec_i = scipy.linalg.eigh(H)
def get_hopping_coulomb():
norbs = 28
Ud, JH = edrixs.UJ_to_UdJH(6, 0.45)
F0_d, F2_d, F4_d = edrixs.UdJH_to_F0F2F4(Ud, JH)
scale_dp = 0.9
G1_dp, G3_dp = 0.894 * scale_dp, 0.531 * scale_dp
F2_dp = 1.036 * scale_dp
Udp_av = 0.0
F0_dp = Udp_av + edrixs.get_F0('dp', G1_dp, G3_dp)
params = [F0_d, F2_d, F4_d]
umat_i = edrixs.get_umat_slater('t2g', *params)
params = [F0_d, F2_d, F4_d, F0_dp, F2_dp, G1_dp, G3_dp, 0.0, 0.0]
umat_tmp = edrixs.get_umat_slater('t2gp', *params)
tmat = np.zeros((12, 12), dtype=np.complex128)
tmat[0:6, 0:6] = edrixs.tmat_c2j(1)
tmat[6:12, 6:12] = edrixs.tmat_c2j(1)
umat_i[:, :, :, :] = edrixs.transform_utensor(umat_i, edrixs.tmat_c2j(1))
umat_tmp[:, :, :, :] = edrixs.transform_utensor(umat_tmp, tmat)
id1 = [0, 1, 2, 3, 4, 5, 8, 9, 10, 11]
id2 = [0, 1, 2, 3, 4, 5, 24, 25, 26, 27]
umat_n = np.zeros((norbs, norbs, norbs, norbs), dtype=np.complex)
for i in range(10):
for j in range(10):
for k in range(10):
for ll in range(10):
umat_n[id2[i], id2[j], id2[k],
id2[ll]] = umat_tmp[id1[i], id1[j], id1[k], id1[ll]]
emat_i = np.zeros((norbs, norbs), dtype=np.complex128)
emat_n = np.zeros((norbs, norbs), dtype=np.complex128)
# bath energy level & hybridization strength
N_site = 3
data = np.loadtxt('bath_sites.in')
e1, v1 = data[:, 0], data[:, 1]
e2, v2 = data[:, 2], data[:, 3]
h = np.zeros((24, 24), dtype=np.complex)
h[0, 0] = h[1, 1] = -14.7627972353
h[2, 2] = h[3, 3] = h[4, 4] = h[5, 5] = -15.4689430453
for i in range(N_site):
o = 6 + 6 * i
# orbital j=1/2
h[o + 0, o + 0] = h[o + 1, o + 1] = e1[i]
h[0, o + 0] = h[1, o + 1] = h[o + 0, 0] = h[o + 1, 1] = v1[i]
# orbital j=3/2
h[o + 2, o + 2] = h[o + 3, o + 3] = h[o + 4, o + 4] = h[o + 5,
o + 5] = e2[i]
h[2, o + 2] = h[3, o + 3] = h[4, o + 4] = h[5, o + 5] = v2[i]
h[o + 2, 2] = h[o + 3, 3] = h[o + 4, 4] = h[o + 5, 5] = v2[i]
emat_i[0:24, 0:24] += h
emat_n[0:24, 0:24] += h
# static core-hole potential
static_V = 2.0
for i in range(6):
emat_n[i, i] -= static_V
# Write to files
# Search GS inputs
edrixs.write_emat(emat_i, "search_gs/hopping_i.in")
edrixs.write_umat(umat_i, "search_gs/coulomb_i.in")
# 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")