def mb_ph_ops(hlat, perturb, omega, nimp, nocc, pemb, pcore, pvirt):
"""
external ops for part-hole Green's function
"""
nimp_sp = nimp * 2
nsites_sp = hlat.shape[0] * 2
nocc_sp = nocc * 2
# transform h into imp+bath/ext(all) basis
pall = N.hstack([pemb, pcore, pvirt])
hall = N.dot(pall.T, N.dot(hlat, pall))
hall_sp = _spinify(hall)
# t1amp in (all) basis
t1amp_ao = make_t1amp_ao(hlat, omega, perturb, nocc)
t1amp_all = N.dot(pall.T, N.dot(t1amp_ao, pall))
t1amp_all_sp = _spinify(t1amp_all)
# mb_ext_operators
sites_imp = range(0, nimp_sp * 2)
sites_ext = range(nimp_sp * 2, nsites_sp)
cops = []
dops = []
project = False
if project:
li_t1amp_ext_imp = _linear_orthonormal_basis(
t1amp_all_sp[sites_ext, :][:, sites_imp], orient='c')
print "retained %i out of %i vectors" % (li_t1amp_ext_imp.shape[1],
len(sites_imp))
li_t1amp_imp_ext = _linear_orthonormal_basis(
t1amp_all_sp[sites_imp, :][:, sites_ext], orient='r')
print "retained %i out of %i vectors" % (li_t1amp_imp_ext.shape[0],
len(sites_imp))
for i in xrange(li_t1amp_ext_imp.shape[1]):
cops.append(models.ContractedC(sites_ext, li_t1amp_ext_imp[:, i]))
for i in xrange(li_t1amp_imp_ext.shape[0]):
dops.append(models.ContractedD(sites_ext, li_t1amp_imp_ext[i, :]))
else:
for imp in sites_imp:
coeff_c = t1amp_all_sp[sites_ext, imp]
cops.append(models.ContractedC(sites_ext, coeff_c))
coeff_d = t1amp_all_sp[imp, sites_ext]
dops.append(models.ContractedD(sites_ext, coeff_d))
cd_coeffs = {}
for i in sites_ext:
for j in sites_ext:
if abs(t1amp_all_sp[i, j]) > 1.e-8:
cd_coeffs[i, j] = t1amp_all_sp[i, j]
cdop = models.ContractedCD(cd_coeffs)
ops = {"1": models.Unit(), "c": cops, "d": dops, "cd": cdop}
return ops
def hubbard_imp_ext_h(h0, u, nocc, nimp, nsites):
nsites_sp = nsites * 2
sites_imp = range(0, 4 * nimp)
sites_ext = range(4 * nimp, 2 * nsites)
t_dict = {}
for i in xrange(nsites_sp):
for j in xrange(nsites_sp):
if abs(h0[i, j]) > 1.e-12:
t_dict[i, j] = h0[i, j]
t_dict[0, 0] = 0
t_dict[1, 1] = 0
u_dict = {}
u_dict[0, 1] = u
# h in imp+ext space
hop = models.GeneralHubbard(t_dict, u_dict)
t_imp = {}
for i in sites_imp:
for j in sites_imp:
if abs(h0[i, j]) > 1.e-12:
t_imp[i, j] = h0[i, j]
t_imp[0, 0] = 0
t_imp[1, 1] = 0
t_ext = {}
for i in sites_ext:
for j in sites_ext:
if abs(h0[i, j]) > 1.e-12:
t_ext[i, j] = h0[i, j]
hext = models.ContractedCD(t_ext)
himp = models.GeneralHubbard(t_imp, u_dict)
hcs_imp = []
hds_imp = []
hcs_ext = []
hds_ext = []
for i in sites_imp:
imp_coeffs = utils.zeros(len(sites_imp))
imp_coeffs[i] = 1.
hcs_imp.append(models.ContractedC(sites_imp, imp_coeffs))
hds_imp.append(models.ContractedD(sites_imp, imp_coeffs))
hcs_ext.append(models.ContractedC(sites_ext, h0[sites_ext, i]))
hds_ext.append(models.ContractedD(sites_ext, h0[i, sites_ext]))
return hop, himp, hcs_imp, hds_imp, hcs_ext, hds_ext, hext
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