def ph_greens():
# main loop for general density-density (ph) response functions
utils.dtype = N.complex128
nimp = 1
nimp_sp = 2 * nimp
nocc = 10
nsites = 20
nsites_sp = nsites * 2
ndim = 2
sz = 0
# sites numbered in order as imp+bath ... ext
sites_imp = range(0, 2 * nimp_sp)
sites_ext = range(2 * nimp_sp, nsites_sp)
ncore = 2 * nocc - 2 * nimp
cocc = range(2 * nimp_sp, 2 * nimp_sp + ncore)
vocc = range(2 * nimp_sp + ncore, nsites_sp)
N.set_printoptions(precision=3)
t = -1. # hopping
delta = 0.0 #25 # broadening
# for u in [0.0,4.0,10.0]:
for u in [0.0, 0.5, 1.0, 2.0, 4.0, 8.0]: #,1.0,4.0,8.0]:
# Single impurity Anderson model
mu = 0.
hlat, hall, hlat_sp, hall_sp, e0 = models_embed.si_anderson_imp_ext_ni_h(
t, nocc, nimp, nsites)
hop, himp, hcs_imp, hds_imp, hcs_ext, hds_ext, hext = models_embed.si_anderson_imp_ext_h(
hall_sp, u, nocc, nimp, nsites)
# single site Hubbard in DMET basis
# mu=u/2
# hlat,hall,hlat_sp,hall_sp,e0=models_embed.hubbard_imp_ext_ni_h(t,u,nocc,nimp,nsites)
# hop,himp,hcs_imp,hds_imp,hcs_ext,hds_ext,hext=models_embed.hubbard_imp_ext_h(hall_sp,u,nocc,nimp,nsites)
# g.s embedding basis
pemb, pcore, pvirt = embed.embed(hlat, nimp, nocc)
# perturbation operator
perturb = utils.zeros([nsites, nsites])
perturb[0, 0] = 1.
p_coeffs = {}
p_coeffs[0, 0] = 1.
p_coeffs[1, 1] = 1.
perturbop = models.ContractedCD(p_coeffs)
fd = file("ph_siam.out." + str(u), "w")
for omega in N.arange(0, 4, 0.01):
if abs(omega - 2.0) < 0.00001:
continue
ops_dict = response_embed.mb_ph_ops(hlat, perturb,
omega + 1j * delta, nimp, nocc,
pemb, pcore, pvirt)
configs_dict = response_embed.mb_configs(nsites, nimp, nimp_sp,
2 * nocc - nimp_sp, 0)
neutral_ops_configs = response_embed.mb_ph_ops_configs(
ops_dict, configs_dict)
# basis is setup, now build matrix representations
perturb_mat = opbasis_ni.oimp_matrix_form(perturbop,
neutral_ops_configs,
cocc, vocc)
# h, neutral configs
himp_mat = opbasis_ni.oimp_matrix_form(himp, neutral_ops_configs,
cocc, vocc)
himp_ext_mat = opbasis_ni.himp_ext_matrix_form(
hcs_imp, hds_ext, hds_imp, hcs_ext, neutral_ops_configs, cocc,
vocc)
hext_mat = opbasis_ni.hext_matrix_form(hext, neutral_ops_configs,
cocc, vocc, e0)
#print 'himp_mat size: ',himp_mat.shape
#print 'himp_mat',himp_mat[:,0]
#print 'hext_mat size: ',hext_mat.shape
#print 'himp_ext_mat size: ',himp_ext_mat.shape
hmat = himp_mat + himp_ext_mat + hext_mat
#print 'total size hmat: ',hmat.shape
unit_mat = opbasis_ni.oimp_matrix_form(models.Unit(),
neutral_ops_configs, cocc,
vocc)
# get neutral ground-state energy
es, cs = la.peigh(hmat, unit_mat)
e0 = es[0]
psi0 = cs[:, 0]
# all matrices setup, solve linear response (complex)
psi1 = la.solve_perturb(omega - 1j * delta,
unit_mat,
hmat,
e0,
psi0,
perturb_mat,
project=True)
ph_gf = N.dot(N.conj(psi1), N.dot(perturb_mat, psi0))
ph_gf0 = _second_order_energy(hlat, nocc, perturb,
omega + 1j * delta)
#print 'hlat size: ',hlat.shape
#print 'hlat: '
#print hlat
#print omega, ph_gf.imag,ph_gf0.imag
print omega, ph_gf, 2 * ph_gf0
print >> fd, omega - mu, ph_gf.imag, ph_gf0.imag, ph_gf.real, 2 * ph_gf0.real
def sp_greens():
# main loop for single-particle GF
utils.dtype = N.complex128
nimp = 1
nimp_sp = 2 * nimp
nocc = 20
nsites = 40
nsites_sp = nsites * 2
ndim = 2
sz = 0
# sites numbered in order as imp+bath ... ext
sites_imp = range(0, 2 * nimp_sp)
sites_ext = range(2 * nimp_sp, nsites_sp)
ncore = 2 * nocc - 2 * nimp
cocc = range(2 * nimp_sp, 2 * nimp_sp + ncore)
vocc = range(2 * nimp_sp + ncore, nsites_sp)
N.set_printoptions(precision=3)
t = -1. # hopping
delta = 0.2 # broadening
# for u in [0.0,4.0,10.0]:
for u in [1.0]:
# Single impurity Anderson model
mu = 0.
hlat, hall, hlat_sp, hall_sp, e0 = models_embed.si_anderson_imp_ext_ni_h(
t, nocc, nimp, nsites)
hop, himp, hcs_imp, hds_imp, hcs_ext, hds_ext, hext = models_embed.si_anderson_imp_ext_h(
hall_sp, u, nocc, nimp, nsites)
# single site Hubbard in DMET basis
# mu=u/2
# hlat,hall,hlat_sp,hall_sp,e0=models_embed.hubbard_imp_ext_ni_h(t,u,nocc,nimp,nsites)
# hop,himp,hcs_imp,hds_imp,hcs_ext,hds_ext,hext=models_embed.hubbard_imp_ext_h(hall_sp,u,nocc,nimp,nsites)
# g.s embedding basis
pemb, pcore, pvirt = embed.embed(hlat, nimp, nocc)
# perturbation operator
perturb = utils.zeros([nsites])
perturb[0] = 1.
p_coeffs = N.array([1])
perturb_dop = models.ContractedD(N.array([0]), p_coeffs)
perturb_cop = models.ContractedC(N.array([0]), p_coeffs)
fd = file("ph_siam.out." + str(u), "w")
for omega in N.arange(-2, 2, 0.1):
ops_dict = response_embed.mb_sp_ops(hlat, perturb,
omega + 1j * delta, nimp, nocc,
pemb, pcore, pvirt)
configs_dict = response_embed.mb_configs(nsites, nimp, nimp_sp,
2 * nocc - nimp_sp, 0)
neutral_ops_configs, plus_ops_configs, minus_ops_configs = response_embed.mb_sp_ops_configs(
ops_dict, configs_dict)
# basis is setup, now build matrix representations
perturb_dop_mat = opbasis_ni.oimp_matrix_bra_ket_form(
perturb_dop, minus_ops_configs, neutral_ops_configs, cocc,
vocc)
perturb_cop_mat = opbasis_ni.oimp_matrix_bra_ket_form(
perturb_cop, plus_ops_configs, neutral_ops_configs, cocc, vocc)
# h, N-1 configs
himp_mat_minus = opbasis_ni.oimp_matrix_form(
himp, minus_ops_configs, cocc, vocc)
himp_ext_mat_minus = opbasis_ni.himp_ext_matrix_form(
hcs_imp, hds_ext, hds_imp, hcs_ext, minus_ops_configs, cocc,
vocc)
hext_mat_minus = opbasis_ni.hext_matrix_form(
hext, minus_ops_configs, cocc, vocc, e0)
hmat_minus = himp_mat_minus + himp_ext_mat_minus + hext_mat_minus
unit_mat_minus = opbasis_ni.oimp_matrix_form(
models.Unit(), minus_ops_configs, cocc, vocc)
# h, N+1 configs
himp_mat_plus = opbasis_ni.oimp_matrix_form(
himp, plus_ops_configs, cocc, vocc)
himp_ext_mat_plus = opbasis_ni.himp_ext_matrix_form(
hcs_imp, hds_ext, hds_imp, hcs_ext, plus_ops_configs, cocc,
vocc)
hext_mat_plus = opbasis_ni.hext_matrix_form(
hext, plus_ops_configs, cocc, vocc, e0)
hmat_plus = himp_mat_plus + himp_ext_mat_plus + hext_mat_plus
unit_mat_plus = opbasis_ni.oimp_matrix_form(
models.Unit(), plus_ops_configs, cocc, vocc)
# h, neutral configs
himp_mat = opbasis_ni.oimp_matrix_form(himp, neutral_ops_configs,
cocc, vocc)
himp_ext_mat = opbasis_ni.himp_ext_matrix_form(
hcs_imp, hds_ext, hds_imp, hcs_ext, neutral_ops_configs, cocc,
vocc)
hext_mat = opbasis_ni.hext_matrix_form(hext, neutral_ops_configs,
cocc, vocc, e0)
hmat = himp_mat + himp_ext_mat + hext_mat
unit_mat = opbasis_ni.oimp_matrix_form(models.Unit(),
neutral_ops_configs, cocc,
vocc)
# get neutral ground-state energy
es, cs = la.peigh(hmat, unit_mat)
e0 = es[0]
psi0 = cs[:, 0]
print e0
print psi0
# all matrices setup, solve linear response (complex)
psi1_minus = la.solve_perturb(omega + 1j * delta,
unit_mat_minus,
hmat_minus,
e0,
psi0,
perturb_dop_mat,
project=False,
sign_ham=-1.)
gfminus = N.dot(psi1_minus, N.dot(perturb_dop_mat, psi0))
psi1_plus = la.solve_perturb(omega + 1j * delta,
unit_mat_plus,
hmat_plus,
e0,
psi0,
perturb_cop_mat,
project=False)
gfplus = N.dot(psi1_plus, N.dot(perturb_cop_mat, psi0))
d_gf, c_gf = _sp_gf(hlat, omega + 1j * delta, perturb, nocc)
print omega, gfplus.imag, c_gf.imag, gfminus.imag, d_gf.imag
print >> fd, omega - mu, gfplus.imag + gfminus.imag, c_gf.imag + d_gf.imag
def main():
# main loop for single-particle GF
utils.dtype = N.complex128
nimp = 4
nimp_sp = 2 * nimp
nsites = 8
nocc = nsites / 2
nsites_sp = nsites * 2
ndim = 2
sz = 0
# sites numbered in order as imp+bath ... ext
sites_imp = range(0, 2 * nimp_sp)
sites_ext = range(2 * nimp_sp, nsites_sp)
ncore = 2 * nocc - 2 * nimp
cocc = range(2 * nimp_sp, 2 * nimp_sp + ncore)
vocc = range(2 * nimp_sp + ncore, nsites_sp)
N.set_printoptions(precision=3)
#t=1. # hopping
gamma = 0.005
rho0 = (nsites - 2) / 2.
t = 0.1 #N.sqrt(gamma/(rho0*N.pi))
#gamma = (t**2)*pi*0.1
delta = 0.005 # broadening
#a=12.5
# for u in [0.0,4.0,10.0]:
for u in [0., 2.5, 5., 7.5]:
u *= t
# Single impurity Anderson model
mu = 0.
hlat, hall, hlat_sp, hall_sp, e0 = models_embed.si_anderson_imp_ext_ni_h(
t, u, nocc, nimp, nsites)
hop, himp, hcs_imp, hds_imp, hcs_ext, hds_ext, hext = models_embed.si_anderson_imp_ext_h(
hall_sp, u, nocc, nimp, nsites)
#print hext
# single site Hubbard in DMET basis
#mu=u/2
#hlat,hall,hlat_sp,hall_sp,e0=models_embed.hubbard_imp_ext_ni_h(t,u,nocc,nimp,nsites)
#hop,himp,hcs_imp,hds_imp,hcs_ext,hds_ext,hext=models_embed.hubbard_imp_ext_h(hall_sp,u,nocc,nimp,nsites)
# g.s embedding basis
pemb, pcore, pvirt = embed.embed(hlat, nimp, nocc)
# perturbation operator
perturb = utils.zeros([nsites])
perturb[0] = 1.
p_coeffs = N.array([1])
perturb_dop = models.ContractedD(N.array([0]), p_coeffs)
perturb_cop = models.ContractedC(N.array([0]), p_coeffs)
fd = file(
"siam_emb_dos_nsites" + str(nsites) + '_U' + str(u) + '_nimp' +
str(nimp) + '_eta' + str(delta), "w")
for omega in N.arange(-1., 1., 0.01):
ops_dict = response_embed.mb_sp_ops(hlat, perturb,
omega + 1j * delta, nimp, nocc,
pemb, pcore, pvirt)
configs_dict = response_embed.mb_configs(nsites, nimp, nimp_sp,
2 * nocc - nimp_sp, 0)
neutral_ops_configs, plus_ops_configs, minus_ops_configs = response_embed.mb_sp_ops_configs(
ops_dict, configs_dict)
#print minus_ops_configs
# basis is setup, now build matrix representations
perturb_dop_mat = opbasis_ni.oimp_matrix_bra_ket_form(
perturb_dop, minus_ops_configs, neutral_ops_configs, cocc,
vocc)
perturb_cop_mat = opbasis_ni.oimp_matrix_bra_ket_form(
perturb_cop, plus_ops_configs, neutral_ops_configs, cocc, vocc)
#print plus_ops_configs
# h, N-1 configs
#print minus_ops_configs
himp_mat_minus = opbasis_ni.oimp_matrix_form(
himp, minus_ops_configs, cocc, vocc)
himp_ext_mat_minus = opbasis_ni.himp_ext_matrix_form(
hcs_imp, hds_ext, hds_imp, hcs_ext, minus_ops_configs, cocc,
vocc)
#print himp_ext_mat_minus
hext_mat_minus = opbasis_ni.hext_matrix_form(
hext, minus_ops_configs, cocc, vocc, e0)
hmat_minus = himp_mat_minus + himp_ext_mat_minus + hext_mat_minus
unit_mat_minus = opbasis_ni.oimp_matrix_form(
models.Unit(), minus_ops_configs, cocc, vocc)
#print hext_mat_minus
# h, N+1 configs
himp_mat_plus = opbasis_ni.oimp_matrix_form(
himp, plus_ops_configs, cocc, vocc)
himp_ext_mat_plus = opbasis_ni.himp_ext_matrix_form(
hcs_imp, hds_ext, hds_imp, hcs_ext, plus_ops_configs, cocc,
vocc)
hext_mat_plus = opbasis_ni.hext_matrix_form(
hext, plus_ops_configs, cocc, vocc, e0)
hmat_plus = himp_mat_plus + himp_ext_mat_plus + hext_mat_plus
unit_mat_plus = opbasis_ni.oimp_matrix_form(
models.Unit(), plus_ops_configs, cocc, vocc)
# h, neutral configs
himp_mat = opbasis_ni.oimp_matrix_form(himp, neutral_ops_configs,
cocc, vocc)
himp_ext_mat = opbasis_ni.himp_ext_matrix_form(
hcs_imp, hds_ext, hds_imp, hcs_ext, neutral_ops_configs, cocc,
vocc)
hext_mat = opbasis_ni.hext_matrix_form(hext, neutral_ops_configs,
cocc, vocc, e0)
hmat = himp_mat + himp_ext_mat + hext_mat
unit_mat = opbasis_ni.oimp_matrix_form(models.Unit(),
neutral_ops_configs, cocc,
vocc)
# get neutral ground-state energy
es, cs = la.peigh(hmat, unit_mat)
e_gs = es[0]
psi0 = cs[:, 0]
#print e0
#print psi0
#print N.dot(perturb_dop_mat,psi0)
# all matrices setup, solve linear response (complex)
psi1_minus = la.solve_perturb(omega + 1j * delta,
unit_mat_minus,
hmat_minus,
e_gs,
psi0,
perturb_dop_mat,
project=False,
sign_ham=-1.)
gfminus = N.dot(psi1_minus, N.dot(perturb_dop_mat, psi0))
psi1_plus = la.solve_perturb(omega + 1j * delta,
unit_mat_plus,
hmat_plus,
e_gs,
psi0,
perturb_cop_mat,
project=False)
#print N.dot(perturb_cop_mat,psi0)
#print hmat
gfplus = N.dot(psi1_plus, N.dot(perturb_cop_mat, psi0))
d_gf, c_gf = _sp_gf(hlat, omega + 1j * delta, perturb, nocc)
#print omega, gfplus.imag,c_gf.imag, gfminus.imag,d_gf.imag
#print >>fd, omega-mu, -1.*(gfplus.imag),-1.*(c_gf.imag+d_gf.imag)
print >> fd, omega - mu, -(1 / N.pi) * (gfplus.imag + gfminus.imag)
def main():
# main loop for single-particle GF
utils.dtype = N.complex128
nimp = 1
nimp_sp = 2 * nimp
nsites = 300
nocc = nsites / 2
nsites_sp = nsites * 2
ndim = 2
sz = 0
# sites numbered in order as imp+bath ... ext
sites_imp = range(0, 2 * nimp_sp)
sites_ext = range(2 * nimp_sp, nsites_sp)
ncore = 2 * nocc - 2 * nimp
cocc = range(2 * nimp_sp, 2 * nimp_sp + ncore)
vocc = range(2 * nimp_sp + ncore, nsites_sp)
N.set_printoptions(precision=3)
#t=1. # hopping
gamma = 0.05
rho0 = (nsites - 2) / 2.
t = N.sqrt(gamma / (rho0 * N.pi))
#t = 0.1
#gamma = (t**2)*pi*0.1
delta = 1e-12 # broadening
#a=12.5
# for u in [0.0,4.0,10.0]:
for u in [10.]:
u *= gamma
# Single impurity Anderson model
mu = 0.
hlat, hall, hlat_sp, hall_sp, e0 = models_embed.si_anderson_imp_ext_ni_h(
t, u, nocc, nimp, nsites)
hop, himp, hcs_imp, hds_imp, hcs_ext, hds_ext, hext = models_embed.si_anderson_imp_ext_h(
hall_sp, u, nocc, nimp, nsites)
#print hext
# single site Hubbard in DMET basis
#mu=u/2
#hlat,hall,hlat_sp,hall_sp,e0=models_embed.hubbard_imp_ext_ni_h(t,u,nocc,nimp,nsites)
#hop,himp,hcs_imp,hds_imp,hcs_ext,hds_ext,hext=models_embed.hubbard_imp_ext_h(hall_sp,u,nocc,nimp,nsites)
# g.s embedding basis
pemb, pcore, pvirt = embed.embed(hlat, nimp, nocc)
# perturbation operator
perturb = utils.zeros([nsites])
perturb[0] = 1.
p_coeffs = N.array([1])
perturb_dop = models.ContractedD(N.array([0]), p_coeffs)
perturb_cop = models.ContractedC(N.array([0]), p_coeffs)
#fd=file("siam_emb_dos_nsites"+str(nsites)+'_U'+str(u)+'_nimp'+str(nimp)+'_eta'+str(delta),"w")
fdEnminus = file("En_minus", "w")
fdCnminus = file("Cn_minus", "w")
fdEnplus = file("En_plus", "w")
fdCnplus = file("Cn_plus", "w")
for omega in [1e-08]: #N.arange(-1.,1.,0.1):
#print omega
ops_dict = response_embed.mb_sp_ops(hlat, perturb,
omega + 1j * delta, nimp, nocc,
pemb, pcore, pvirt)
configs_dict = response_embed.mb_configs(nsites, nimp, nimp_sp,
2 * nocc - nimp_sp, 0)
neutral_ops_configs, plus_ops_configs, minus_ops_configs = response_embed.mb_sp_ops_configs(
ops_dict, configs_dict)
#print _ops_configs
# basis is setup, now build matrix representations
perturb_dop_mat = opbasis_ni.oimp_matrix_bra_ket_form(
perturb_dop, minus_ops_configs, neutral_ops_configs, cocc,
vocc)
perturb_cop_mat = opbasis_ni.oimp_matrix_bra_ket_form(
perturb_cop, plus_ops_configs, neutral_ops_configs, cocc, vocc)
# h, N-1 configs
#print ops_dict['d'][0]
himp_mat_minus = opbasis_ni.oimp_matrix_form(
himp, minus_ops_configs, cocc, vocc)
himp_ext_mat_minus = opbasis_ni.himp_ext_matrix_form(
hcs_imp, hds_ext, hds_imp, hcs_ext, minus_ops_configs, cocc,
vocc)
#print himp_ext_mat_minus
hext_mat_minus = opbasis_ni.hext_matrix_form(
hext, minus_ops_configs, cocc, vocc, e0)
hmat_minus = himp_mat_minus + himp_ext_mat_minus + hext_mat_minus
unit_mat_minus = opbasis_ni.oimp_matrix_form(
models.Unit(), minus_ops_configs, cocc, vocc)
#print hext_mat_minus
# h, N+1 configs
himp_mat_plus = opbasis_ni.oimp_matrix_form(
himp, plus_ops_configs, cocc, vocc)
himp_ext_mat_plus = opbasis_ni.himp_ext_matrix_form(
hcs_imp, hds_ext, hds_imp, hcs_ext, plus_ops_configs, cocc,
vocc)
hext_mat_plus = opbasis_ni.hext_matrix_form(
hext, plus_ops_configs, cocc, vocc, e0)
hmat_plus = himp_mat_plus + himp_ext_mat_plus + hext_mat_plus
unit_mat_plus = opbasis_ni.oimp_matrix_form(
models.Unit(), plus_ops_configs, cocc, vocc)
# h, neutral configs
himp_mat = opbasis_ni.oimp_matrix_form(himp, neutral_ops_configs,
cocc, vocc)
himp_ext_mat = opbasis_ni.himp_ext_matrix_form(
hcs_imp, hds_ext, hds_imp, hcs_ext, neutral_ops_configs, cocc,
vocc)
hext_mat = opbasis_ni.hext_matrix_form(hext, neutral_ops_configs,
cocc, vocc, e0)
hmat = himp_mat + himp_ext_mat + hext_mat
unit_mat = opbasis_ni.oimp_matrix_form(models.Unit(),
neutral_ops_configs, cocc,
vocc)
#print hext_mat_minus
# get neutral ground-state energy
es, cs = la.peigh(hmat, unit_mat)
e_gs = es[0]
psi0 = cs[:, 0]
es_minus, cs_minus = la.peigh(hmat_minus, unit_mat_minus)
Enarray = es_minus - e_gs * N.ones(len(es_minus))
print >> fdEnminus, omega, str(list(Enarray))[1:-1].translate(
None, ',')
es_plus, cs_plus = la.peigh(hmat_plus, unit_mat_plus)
Enarray = es_plus - e_gs * N.ones(len(es_minus))
print >> fdEnplus, omega, str(list(Enarray))[1:-1].translate(
None, ',')
gfminus = 0.
mat_el_list_minus = []
for i in xrange(len(es_minus)):
ket = N.dot(perturb_dop_mat, psi0)
bra = N.transpose(cs_minus[:, i].conjugate())
mat_el = N.dot(bra, ket)
mat_el *= mat_el.conjugate()
mat_el_list_minus.append(mat_el.real)
den = omega + 1j * delta - e_gs + es_minus[i]
gfminus += (mat_el / den)
print >> fdCnminus, omega, str(mat_el_list_minus)[1:-1].translate(
None, ',')
gfplus = 0.
mat_el_list_plus = []
for i in xrange(len(es_plus)):
ket = N.dot(perturb_cop_mat, psi0)
bra = N.transpose(cs_plus[:, i].conjugate())
mat_el = N.dot(bra, ket)
mat_el *= mat_el.conjugate()
mat_el_list_plus.append(mat_el.real)
den = omega + 1j * delta + e_gs - es_plus[i]
gfplus += (mat_el / den)
print >> fdCnplus, omega, str(mat_el_list_plus)[1:-1].translate(
None, ',')
def ph_greens():
# main loop for general density-density (ph) response functions
utils.dtype=N.complex128
nimp=2
nimp_sp=2*nimp
nocc=12
nsites=24
nsites_sp=nsites*2
ndim=2
sz=0
# sites numbered in order as imp+bath ... ext
sites_imp=range(0,2*nimp_sp)
sites_ext=range(2*nimp_sp,nsites_sp)
ncore=2*nocc-2*nimp
cocc=range(2*nimp_sp,2*nimp_sp+ncore)
vocc=range(2*nimp_sp+ncore,nsites_sp)
N.set_printoptions(precision=3)
t=-1. # hopping
delta=0.01 # broadening
# for u in [0.0,4.0,10.0]:
for u in [4.0]:
# Single impurity Anderson model
mu=0.
hlat,hall,hlat_sp,hall_sp,e0=models_embed.si_anderson_imp_ext_ni_h(t,nocc,nimp,nsites)
hop,himp,hcs_imp,hds_imp,hcs_ext,hds_ext,hext=models_embed.si_anderson_imp_ext_h(hall_sp,u,nocc,nimp,nsites)
# single site Hubbard in DMET basis
# mu=u/2
# hlat,hall,hlat_sp,hall_sp,e0=models_embed.hubbard_imp_ext_ni_h(t,u,nocc,nimp,nsites)
# hop,himp,hcs_imp,hds_imp,hcs_ext,hds_ext,hext=models_embed.hubbard_imp_ext_h(hall_sp,u,nocc,nimp,nsites)
# g.s embedding basis
pemb,pcore,pvirt=embed.embed(hlat,nimp,nocc)
# perturbation operator
perturb=utils.zeros([nsites,nsites])
perturb[0,0]=1.
p_coeffs={}
p_coeffs[0,0]=1.
p_coeffs[1,1]=1.
perturbop=models.ContractedCD(p_coeffs)
fd=file("ph_siam.out."+str(u),"w")
for omega in N.arange(2.0,8.0,0.1):
ops_dict=response_embed.mb_ph_ops(hlat,perturb,omega+1j*delta,nimp,nocc,pemb,pcore,pvirt)
configs_dict=response_embed.mb_configs(nsites,nimp,nimp_sp,2*nocc-nimp_sp,0)
neutral_ops_configs=response_embed.mb_ph_ops_configs(ops_dict,configs_dict)
# basis is setup, now build matrix representations
perturb_mat=opbasis_ni.oimp_matrix_form(perturbop,neutral_ops_configs,cocc,vocc)
# h, neutral configs
himp_mat=opbasis_ni.oimp_matrix_form(himp,neutral_ops_configs,cocc,vocc)
himp_ext_mat=opbasis_ni.himp_ext_matrix_form(hcs_imp,hds_ext,hds_imp,hcs_ext,neutral_ops_configs,cocc,vocc)
hext_mat=opbasis_ni.hext_matrix_form(hext,neutral_ops_configs,cocc,vocc,e0)
hmat=himp_mat+himp_ext_mat+hext_mat
unit_mat=opbasis_ni.oimp_matrix_form(models.Unit(),neutral_ops_configs,cocc,vocc)
# get neutral ground-state energy
# print 'overlap: '
# for i,w in enumerate(unit_mat):
# for j,v in enumerate(w):
# if abs(unit_mat[i,j]) > 1.e-12:
# print i+1,j+1,unit_mat[i,j]
#hmat[4:,:] = 0.
#hmat[:,4:] = 0.
#print 'hamil: '
#for i,w in enumerate(hmat):
# for j,v in enumerate(w):
# if abs(hmat[i,j]) > 1.e-12:
# print i+1,j+1,hmat[i,j]
#
es,cs=la.peigh(hmat,unit_mat,thresh=1.e-10)
e0=es[0]
psi0=cs[:,0]
#print 'psi0:'
#print psi0
#print 'energy: ',e0
# all matrices setup, solve linear response (complex)
psi1=la.solve_perturb(omega-1j*delta,unit_mat,hmat,e0,psi0,perturb_mat,project=True)
ph_gf=N.dot(N.conj(psi1),N.dot(perturb_mat,psi0))
ph_gf0=_second_order_energy(hlat,nocc,perturb,omega+1j*delta)
#print omega, ph_gf.imag,ph_gf0.imag
print omega, ph_gf,2*ph_gf0,e0
print >>fd, omega-mu, -ph_gf.imag,-2*ph_gf0.imag
def sp_greens():
# main loop for single-particle GF
utils.dtype=N.complex128
nimp=1
nimp_sp=2*nimp
nocc=20
nsites=40
nsites_sp=nsites*2
ndim=2
sz=0
# sites numbered in order as imp+bath ... ext
sites_imp=range(0,2*nimp_sp)
sites_ext=range(2*nimp_sp,nsites_sp)
ncore=2*nocc-2*nimp
cocc=range(2*nimp_sp,2*nimp_sp+ncore)
vocc=range(2*nimp_sp+ncore,nsites_sp)
N.set_printoptions(precision=3)
t=-1. # hopping
delta=0.2 # broadening
# for u in [0.0,4.0,10.0]:
for u in [1.0]:
# Single impurity Anderson model
mu=0.
hlat,hall,hlat_sp,hall_sp,e0=models_embed.si_anderson_imp_ext_ni_h(t,nocc,nimp,nsites)
hop,himp,hcs_imp,hds_imp,hcs_ext,hds_ext,hext=models_embed.si_anderson_imp_ext_h(hall_sp,u,nocc,nimp,nsites)
# single site Hubbard in DMET basis
# mu=u/2
# hlat,hall,hlat_sp,hall_sp,e0=models_embed.hubbard_imp_ext_ni_h(t,u,nocc,nimp,nsites)
# hop,himp,hcs_imp,hds_imp,hcs_ext,hds_ext,hext=models_embed.hubbard_imp_ext_h(hall_sp,u,nocc,nimp,nsites)
# g.s embedding basis
pemb,pcore,pvirt=embed.embed(hlat,nimp,nocc)
# perturbation operator
perturb=utils.zeros([nsites])
perturb[0]=1.
p_coeffs=N.array([1])
perturb_dop=models.ContractedD(N.array([0]),p_coeffs)
perturb_cop=models.ContractedC(N.array([0]),p_coeffs)
fd=file("ph_siam.out."+str(u),"w")
for omega in N.arange(-2,2,0.1):
ops_dict=response_embed.mb_sp_ops(hlat,perturb,omega+1j*delta,nimp,nocc,pemb,pcore,pvirt)
configs_dict=response_embed.mb_configs(nsites,nimp,nimp_sp,2*nocc-nimp_sp,0)
neutral_ops_configs,plus_ops_configs,minus_ops_configs=response_embed.mb_sp_ops_configs(ops_dict,configs_dict)
# basis is setup, now build matrix representations
perturb_dop_mat=opbasis_ni.oimp_matrix_bra_ket_form(perturb_dop,minus_ops_configs,neutral_ops_configs,cocc,vocc)
perturb_cop_mat=opbasis_ni.oimp_matrix_bra_ket_form(perturb_cop,plus_ops_configs,neutral_ops_configs,cocc,vocc)
# h, N-1 configs
himp_mat_minus=opbasis_ni.oimp_matrix_form(himp,minus_ops_configs,cocc,vocc)
himp_ext_mat_minus=opbasis_ni.himp_ext_matrix_form(hcs_imp,hds_ext,hds_imp,hcs_ext,minus_ops_configs,cocc,vocc)
hext_mat_minus=opbasis_ni.hext_matrix_form(hext,minus_ops_configs,cocc,vocc,e0)
hmat_minus=himp_mat_minus+himp_ext_mat_minus+hext_mat_minus
unit_mat_minus=opbasis_ni.oimp_matrix_form(models.Unit(),minus_ops_configs,cocc,vocc)
# h, N+1 configs
himp_mat_plus=opbasis_ni.oimp_matrix_form(himp,plus_ops_configs,cocc,vocc)
himp_ext_mat_plus=opbasis_ni.himp_ext_matrix_form(hcs_imp,hds_ext,hds_imp,hcs_ext,plus_ops_configs,cocc,vocc)
hext_mat_plus=opbasis_ni.hext_matrix_form(hext,plus_ops_configs,cocc,vocc,e0)
hmat_plus=himp_mat_plus+himp_ext_mat_plus+hext_mat_plus
unit_mat_plus=opbasis_ni.oimp_matrix_form(models.Unit(),plus_ops_configs,cocc,vocc)
# h, neutral configs
himp_mat=opbasis_ni.oimp_matrix_form(himp,neutral_ops_configs,cocc,vocc)
himp_ext_mat=opbasis_ni.himp_ext_matrix_form(hcs_imp,hds_ext,hds_imp,hcs_ext,neutral_ops_configs,cocc,vocc)
hext_mat=opbasis_ni.hext_matrix_form(hext,neutral_ops_configs,cocc,vocc,e0)
hmat=himp_mat+himp_ext_mat+hext_mat
unit_mat=opbasis_ni.oimp_matrix_form(models.Unit(),neutral_ops_configs,cocc,vocc)
# get neutral ground-state energy
es,cs=la.peigh(hmat,unit_mat)
e0=es[0]
psi0=cs[:,0]
print e0
print psi0
# all matrices setup, solve linear response (complex)
psi1_minus=la.solve_perturb(omega+1j*delta,unit_mat_minus,hmat_minus,e0,psi0,perturb_dop_mat,
project=False,sign_ham=-1.)
gfminus=N.dot(psi1_minus,N.dot(perturb_dop_mat,psi0))
psi1_plus=la.solve_perturb(omega+1j*delta,unit_mat_plus,hmat_plus,e0,psi0,perturb_cop_mat,project=False)
gfplus=N.dot(psi1_plus,N.dot(perturb_cop_mat,psi0))
d_gf,c_gf=_sp_gf(hlat,omega+1j*delta,perturb,nocc)
print omega, gfplus.imag,c_gf.imag, gfminus.imag,d_gf.imag
print >>fd, omega-mu, gfplus.imag+gfminus.imag,c_gf.imag+d_gf.imag
