# The atomic Coulomb interactions are usually initialized based on Hartree-Fock
# calculations from, for example,
# `Cowan's code <https://www.tcd.ie/Physics/people/Cormac.McGuinness/Cowan/>`_.
# edrixs has a database of these.
info = edrixs.utils.get_atom_data('Ni', '3d', nd, edge='L3')
################################################################################
# The atomic values are typically scaled to account for screening in the solid.
# Here we use 80% scaling. Let's write these out in full, so that nothing is
# hidden. Values for :math:`U_{dd}` and :math:`U_{dp}` are those of Ref. [1]_
# obtained by comparing theory and experiment [2]_ [3]_.
scale_dd = 0.8
F2_dd = info['slater_i'][1][1] * scale_dd
F4_dd = info['slater_i'][2][1] * scale_dd
U_dd = 7.3
F0_dd = U_dd + edrixs.get_F0('d', F2_dd, F4_dd)
scale_dp = 0.8
F2_dp = info['slater_n'][4][1] * scale_dp
G1_dp = info['slater_n'][5][1] * scale_dp
G3_dp = info['slater_n'][6][1] * scale_dp
U_dp = 8.5
F0_dp = U_dp + edrixs.get_F0('dp', G1_dp, G3_dp)
slater = ([F0_dd, F2_dd, F4_dd], # initial
[F0_dd, F2_dd, F4_dd, F0_dp, F2_dp, G1_dp, G3_dp]) # with core hole
################################################################################
# Charge-transfer energy scales
# ------------------------------------------------------------------------------
# The charge-transfer :math:`\Delta` and Coulomb :math:`U_{dd}` :math:`U_{dp}`
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")
from mpi4py import MPI
if __name__ == "__main__":
'''
Valence shells: 3d4p, Core shell: 2p
Ni :math:`L_{2,3}`-edge, :math:`2p_{1/2,3/2}\\rightarrow 3d` transition.
Used to test the ed_2v1c_fort, xas_2v1c_fort, rixs_2v1c_fort solvers.
How to run
----------
mpiexec -n 2 python test_2v1c.py
'''
F2_dd, F4_dd = 12.234 * 0.65, 7.598 * 0.65
F0_dd = edrixs.get_F0('d', F2_dd, F4_dd)
G1_d4p, G3_d4p = 5.787 * 0.7, 3.291 * 0.7
F0_d4p = edrixs.get_F0('dp', G1_d4p, G3_d4p)
F2_d4p = 7.721 * 0.95
F0_4p4p, F2_4p4p = 0.0, 0.0
F2_d2p = 7.721 * 0.95
G1_d2p, G3_d2p = 5.787 * 0.7, 3.291 * 0.7
F0_d2p = edrixs.get_F0('dp', G1_d2p, G3_d2p)
F0_4p2p = 2.0
F2_4p2p = 2.0
G0_4p2p = 2.0
G2_4p2p = 2.0
v_noccu=(noccu, 0),
edge='L3',
trans_to_which=2,
label=('f', 'd', 'p'))
if rank == 0:
print(res, flush=True)
# Slater integrals
si = collections.OrderedDict(res['slater_i'])
sn = collections.OrderedDict(res['slater_n'])
# Initial Hamiltonian, 5f-5f
si['F2_ff'] = si['F2_ff'] * 0.77
si['F4_ff'] = si['F4_ff'] * 0.77
si['F6_ff'] = si['F6_ff'] * 0.77
si['F0_ff'] = edrixs.get_F0('f', si['F2_ff'], si['F4_ff'], si['F6_ff'])
# Intermediate Hamiltonian, 5f-5f
sn['F2_ff'] = sn['F2_ff'] * 0.77
sn['F4_ff'] = sn['F4_ff'] * 0.77
sn['F6_ff'] = sn['F6_ff'] * 0.77
sn['F0_ff'] = edrixs.get_F0('f', sn['F2_ff'], sn['F4_ff'], sn['F6_ff'])
# 5f-6d
sn['F0_fd'] = edrixs.get_F0('fd', sn['G1_fd'], sn['G3_fd'], sn['G5_fd'])
# 5f-2p
sn['F0_fp'] = edrixs.get_F0('fp', sn['G2_fp'], sn['G4_fp'])
# 6d-2p
sn['F0_dp'] = edrixs.get_F0('dp', sn['G1_dp'], sn['G3_dp'])
slater = (list(si.values()), list(sn.values()))
[-2.0 / 3.0, -2.0 / 3.0, +1.0 / 3.0]]).T
loc_axis[1] = np.array([[+2.0 / 3.0, -1.0 / 3.0, -2.0 / 3.0],
[-1.0 / 3.0, +2.0 / 3.0, -2.0 / 3.0],
[+2.0 / 3.0, +2.0 / 3.0, +1.0 / 3.0]]).T
loc_axis[2] = np.array([[+2.0 / 3.0, -2.0 / 3.0, -1.0 / 3.0],
[+2.0 / 3.0, +1.0 / 3.0, +2.0 / 3.0],
[-1.0 / 3.0, -2.0 / 3.0, +2.0 / 3.0]]).T
loc_axis[3] = np.array([[-2.0 / 3.0, +2.0 / 3.0, -1.0 / 3.0],
[-2.0 / 3.0, -1.0 / 3.0, +2.0 / 3.0],
[+1.0 / 3.0, +2.0 / 3.0, +2.0 / 3.0]]).T
# Kanamori U, J
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)
F0_dd = edrixs.get_F0('d', F2_dd, F4_dd)
G1_dp, G3_dp = 0.957, 0.569
F0_dp, F2_dp = edrixs.get_F0('dp', G1_dp, G3_dp), 1.107
slater = (
[F0_dd, F2_dd, F4_dd], # Initial
[F0_dd, F2_dd, F4_dd, F0_dp, F2_dp, G1_dp, G3_dp] # Intermediate
)
# SOC of 5d
zeta_d = 0.45
# Trigonal crystal field
cf = edrixs.cf_trigonal_t2g(-0.15)
import matplotlib.pyplot as plt
import matplotlib as mpl
import edrixs
# Setup parameters
# ----------------
# Number of occupancy of 3d shell
noccu = 8
res = edrixs.get_atom_data('Ni', v_name='3d', v_noccu=noccu, edge='L23')
name_i, slat_i = [list(i) for i in zip(*res['slater_i'])]
name_n, slat_n = [list(i) for i in zip(*res['slater_n'])]
# Slater integrals for initial Hamiltonian without core-hole
si = edrixs.rescale(slat_i, ([1, 2], [0.65] * 2))
si[0] = edrixs.get_F0('d', si[1], si[2]) # F0_dd
# Slater integrals for intermediate Hamiltonian with core-hole
sn = edrixs.rescale(slat_n, ([1, 2, 4, 5, 6], [0.65, 0.65, 0.95, 0.7, 0.7]))
sn[0] = edrixs.get_F0('d', sn[1], sn[2]) # F0_dd
sn[3] = edrixs.get_F0('dp', sn[5], sn[6]) # F0_dp
slater = (si, sn)
# Spin-orbit coupling strengths
zeta_d_i = res['v_soc_i'][0] # valence 3d electron without core-hole
zeta_d_n = res['v_soc_n'][0] # valence 3d electron with core-hole
# E_{L2} - E_{L3} = 1.5 * zeta_p
zeta_p_n = (res['edge_ene'][0] - res['edge_ene'][1]) / 1.5 # core 2p electron
# Tetragonal crystal field
How to run
----------
mpiexec -n 4 python run_rixs_fsolver.py
'''
# PARAMETERS
# -----------
# Occupancy of U 5f orbitals
noccu = 6
res = edrixs.get_atom_data('Pu', v_name='5f', v_noccu=noccu, edge='O45')
name_i, slat_i = [list(i) for i in zip(*res['slater_i'])]
name_n, slat_n = [list(i) for i in zip(*res['slater_n'])]
# Initial Hamiltonian
si = edrixs.rescale(slat_i, ([1, 2, 3], [0.77] * 3))
si[0] = edrixs.get_F0('f', si[1], si[2], si[3])
# Intermediate Hamiltonian
sn = edrixs.rescale(slat_n,
([1, 2, 3, 5, 6, 7, 8, 9], [0.77] * 3 + [0.6] * 4))
sn[0] = edrixs.get_F0('f', sn[1], sn[2], sn[3])
sn[4] = edrixs.get_F0('fd', sn[7], sn[8], sn[9])
slater = (si, sn)
# Spin-Orbit Coupling (SOC) zeta
# 5f, without core-hole, from Cowan's code
zeta_f_i = res['v_soc_i'][0] * 0.9
# 5f, with core-hole, from Cowan's code
zeta_f_n = res['v_soc_n'][0] * 0.9
zeta_d_n = (res['edge_ene'][0] - res['edge_ene'][1]) / 2.5
def do_ed(dq10=1.6, d1=0.1, d3=0.75, ex_x=0., ex_y=0., ex_z=0.):
"""
Diagonalize Hamiltonian for Ni 3d8 system in tetragonal crytals field and
applied exchange field.
Parameters
----------
dq10: float
Cubic crystal field parameter (eV)
Cubic splitting
dq1: float
Cubic crystal field parameter (eV)
t2g splitting
dq3: float
Cubic crystal field parameter (eV)
eg splitting
ex_x: float
Magnitude of the magnetic exchange field in the x direction (eV)
ex_y: float
Magnitude of the magnetic exchange field in the y direction (eV)
ex_z: float
Magnitude of the magnetic exchange field in the z direction (eV)
Returns
--------
eval_i: 1d array
Eigenvalues of initial state Hamiltonian
eval_n: 1d array
Eigenvalues of intermediate state Hamiltonian
dipole_op: 3d array
Dipole operator from 2p to 3d state
"""
# PARAMETERS:
# ------------
F2_dd, F4_dd = 12.234 * 0.65, 7.598 * 0.65
Ud_av = 0.0
F0_dd = Ud_av + edrixs.get_F0('d', F2_dd, F4_dd)
G1_dp, G3_dp = 5.787 * 0.7, 3.291 * 0.7
F2_dp = 7.721 * 0.95
Udp_av = 0.0
F0_dp = Udp_av + edrixs.get_F0('dp', G1_dp, G3_dp)
slater = (
[F0_dd, F2_dd, F4_dd], # Initial
[F0_dd, F2_dd, F4_dd, F0_dp, F2_dp, G1_dp, G3_dp] # Intermediate
)
zeta_d_i = 0.083
zeta_d_n = 0.102
zeta_p_n = 11.24
cf = edrixs.cf_tetragonal_d(dq10, d1, d3)
ext_B = np.array([ex_x, ex_y, ex_z])
result = edrixs.ed_1v1c_py(shell_name=('d', 'p'),
v_soc=(zeta_d_i, zeta_d_n),
c_soc=zeta_p_n,
v_noccu=8,
slater=slater,
ext_B=ext_B,
on_which='spin',
v_cfmat=cf)
return result
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
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")
#!/usr/bin/env python
import scipy
import numpy as np
import edrixs
if __name__ == "__main__":
norbs = 24
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
zeta_d_i, zeta_p_n = 0.35, 1072.6666666666667
Ir_loc2g = np.zeros((2, 3, 3), dtype=np.float64)
Ir_loc2g[0] = [[+0.70710678, +0.40824829, +0.57735027],
[-0.70710678, +0.40824829, +0.57735027],
[+0.00000000, -0.81649658, +0.57735027]]
Ir_loc2g[1] = [
[-0.70710678, +0.40824829, -0.57735027],
[+0.70710678, +0.40824829, -0.57735027],
[+0.00000000, -0.81649658, -0.57735027],
]
umat_t2g_i = edrixs.get_umat_slater('t2g', F0_d, F2_d, F4_d)
umat_t2g_i = edrixs.transform_utensor(umat_t2g_i,
edrixs.tmat_c2r('t2g', True))
params = [
1 impuirty site plus 3 bath sites
How to run
----------
mpiexec -n 4 python run_rixs_fsolver.py
"""
U, J = 6.0, 0.45 # Kanamori U, J
Ud, JH = edrixs.UJ_to_UdJH(U, J)
F0_dd, F2_dd, F4_dd = 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)
slater = (
[F0_dd, F2_dd, F4_dd], # initial
[F0_dd, F2_dd, F4_dd, F0_dp, F2_dp, G1_dp, G3_dp]) # intermediate
nbath = 3 # number of bath sites
norb = 6 # number of orbitals for each site
# bath energy level & hybridization strength
bath_level = np.zeros((nbath, norb), dtype=np.complex)
hyb = np.zeros((nbath, norb), dtype=np.complex)
e1 = [-3.528372861516216, -1.207615555008166, 6.183392524170465]
e2 = [-3.538890277572901, -1.308137924011529, 5.578400781316763]
v1 = [2.131943931119928, 0.481470627582356, 1.618130554107574]
v2 = [2.108388983547592, 0.517200653226272, 1.674013405873617]
# PARAMETERS
# -----------
# The parameters used in this calculation are taken from [PRL 114, 236401 (2015)]
# 14 5f-orbitals, 10 5d-orbitals (including spin)
# Slater integrals
# The Slater integrals are calculated by the Cowan's code:
# [https://www.tcd.ie/Physics/people/Cormac.McGuinness/Cowan/]
# by using Hartree-Fock mean-field method, and then re-scaled,
# for example, Fff: 77%, Ffd: 60%, Gfd: 60%
F2_ff, F4_ff, F6_ff = 9.711 * 0.77, 6.364 * 0.77, 4.677 * 0.77
# Here, Uf_av is the averaged Coulomb interaction in 5f shell, we set it to be zero
# It doesn't matter here because we are doing single atomic calculation with fixed 5f occupancy.
Uf_av = 0.0
# F0_ff is split into two parts: (1) Uf_av, (2) related to F2_f, F4_f, F6_f
F0_ff = Uf_av + edrixs.get_F0('f', F2_ff, F4_ff, F6_ff)
F2_fd, F4_fd = 10.652 * 0.6, 6.850 * 0.6
G1_fd, G3_fd, G5_fd = 12.555 * 0.6, 7.768 * 0.6, 5.544 * 0.6
Ufd_av = 0.0
F0_fd = Ufd_av + edrixs.get_F0('fd', G1_fd, G3_fd, G5_fd)
slater = (
[F0_ff, F2_ff, F4_ff, F6_ff], # Initial
[F0_ff, F2_ff, F4_ff, F6_ff, F0_fd, F2_fd, F4_fd, G1_fd, G3_fd, G5_fd] # Intermediate
)
# Spin-Orbit Coupling (SOC) zeta
# 5f, without core-hole, from Cowan's code
zeta_f_i = 0.261 * 0.9
# 5f, with core-hole, from Cowan's code
zeta_f_n = 0.274 * 0.9
# Slater parameters
# ------------------------------------------------------------------------------
# Here we want to use Hund's interaction
# :math:`J_H` and spin orbit coupling :math:`\lambda` as adjustable parameters
# to match experiment. We will take
# the core hole interaction parameter from the Hartree Fock numbers EDRIXS has
# in its database. These need to be converted and arranged into the order
# required by EDRIXS.
Ud = 2
JH = 0.25
lam = 0.42
F0_d, F2_d, F4_d = edrixs.UdJH_to_F0F2F4(Ud, JH)
info = edrixs.utils.get_atom_data('Ir', '5d', v_noccu, edge='L3')
G1_dp = info['slater_n'][5][1]
G3_dp = info['slater_n'][6][1]
F0_dp = edrixs.get_F0('dp', G1_dp, G3_dp)
F2_dp = info['slater_n'][4][1]
slater_i = [F0_d, F2_d, F4_d] # Fk for d
slater_n = [
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
]
slater = [slater_i, slater_n]
v_soc = (lam, lam)
################################################################################
# Diagonalization
# ------------------------------------------------------------------------------
"""
Do exact diagonalization of a f electronic system with 14 orbitals.
You can change noccu to play with it.
"""
# number of orbitals
norbs = 14
# number of occupancy, change this number and re-run it to see how it will change.
noccu = 7
# Slater integrals: FX, x=0, 2, 4, 2*3=6
F2_f, F4_f, F6_f = 9.711 * 0.77, 6.364 * 0.77, 4.677 * 0.77
# set the average Coulomb interaction energy Uf_ave to zero
Uf_av = 0.0
F0_f = Uf_av + edrixs.get_F0('f', F2_f, F4_f, F6_f)
# get rank-4 Coulomb U-tensor
params = [F0_f, F2_f, F4_f, F6_f]
umat_i = edrixs.get_umat_slater('f', *params)
# 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)
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")
