def solve_lattice_bse_e_k_sigma_w(mu,
e_k,
sigma_w,
gamma_wnn,
tail_corr_nwf=-1):
kmesh = e_k.mesh
fmesh_huge = sigma_w.mesh
bmesh = gamma_wnn.mesh.components[0]
fmesh = gamma_wnn.mesh.components[1]
nk = len(kmesh)
nw = (len(bmesh) + 1) / 2
nwf = len(fmesh) / 2
nwf_sigma = len(fmesh_huge) / 2
if mpi.is_master_node():
print tprf_banner(), "\n"
print 'Lattcie BSE with local vertex approximation.\n'
print 'nk =', nk
print 'nw =', nw
print 'nwf =', nwf
print 'nwf_sigma =', nwf_sigma
print 'nwf_chi0_tail =', tail_corr_nwf
print
# -- Lattice BSE calc with built in trace using g_wk
from triqs_tprf.lattice import chiq_sum_nu_from_e_k_sigma_w_and_gamma_PH
chi_kw = chiq_sum_nu_from_e_k_sigma_w_and_gamma_PH(
mu, e_k, sigma_w, gamma_wnn, tail_corr_nwf=tail_corr_nwf)
return chi_kw
def bubble_setup(beta, mu, tb_lattice, nk, nw, sigma_w=None):
print tprf_banner(), "\n"
print 'beta =', beta
print 'mu =', mu
print 'sigma =', (not (sigma == None))
norb = tb_lattice.NOrbitalsInUnitCell
print 'nk =', nk
print 'nw =', nw
print 'norb =', norb
print
ntau = 4 * nw
ntot = np.prod(nk) * norb**4 + np.prod(nk) * (nw + ntau) * norb**2
nbytes = ntot * np.complex128().nbytes
ngb = nbytes / 1024.**3
print 'Approx. Memory Utilization: %2.2f GB\n' % ngb
periodization_matrix = np.diag(np.array(list(nk), dtype=np.int32))
#print 'periodization_matrix =\n', periodization_matrix
bz = BrillouinZone(tb_lattice.bl)
bzmesh = MeshBrillouinZone(bz, periodization_matrix)
print '--> ek'
e_k = ek_tb_dispersion_on_bzmesh(tb_lattice, bzmesh, bz)
if sigma is None:
print '--> g0k'
wmesh = MeshImFreq(beta=beta, S='Fermion', n_max=nw)
g_wk = lattice_dyson_g0_wk(mu=mu, e_k=e_k, mesh=wmesh)
else:
print '--> gk'
sigma_w = strip_sigma(nw, beta, sigma)
g_wk = lattice_dyson_g_wk(mu=mu, e_k=e_k, sigma_w=sigma_w)
print '--> gr_from_gk (k->r)'
g_wr = fourier_wk_to_wr(g_wk)
del g_wk
print '--> grt_from_grw (w->tau)'
g_tr = fourier_wr_to_tr(g_wr)
del g_wr
if sigma is None:
return g_tr
else:
return g_tr, sigma_w
def imtime_bubble_chi0_wk(g_wk, nw=1):
wmesh, kmesh = g_wk.mesh.components
norb = g_wk.target_shape[0]
beta = wmesh.beta
nw_g = len(wmesh)
nk = len(kmesh)
ntau = 4 * nw_g
ntot = np.prod(nk) * norb**4 + np.prod(nk) * (nw_g + ntau) * norb**2
nbytes = ntot * np.complex128().nbytes
ngb = nbytes / 1024.**3
if mpi.is_master_node():
print tprf_banner(), "\n"
print 'beta =', beta
print 'nk =', nk
print 'nw =', nw_g
print 'norb =', norb
print
print 'Approx. Memory Utilization: %2.2f GB\n' % ngb
mpi.report('--> fourier_wk_to_wr')
g_wr = fourier_wk_to_wr(g_wk)
del g_wk
mpi.report('--> fourier_wr_to_tr')
g_tr = fourier_wr_to_tr(g_wr)
del g_wr
if nw == 1:
mpi.report('--> chi0_w0r_from_grt_PH (bubble in tau & r)')
chi0_wr = chi0_w0r_from_grt_PH(g_tr)
del g_tr
else:
mpi.report('--> chi0_tr_from_grt_PH (bubble in tau & r)')
chi0_tr = chi0_tr_from_grt_PH(g_tr)
del g_tr
mpi.report('--> chi_wr_from_chi_tr')
chi0_wr = chi_wr_from_chi_tr(chi0_tr, nw=nw)
del chi_tr
mpi.report('--> chi_wk_from_chi_wr (r->k)')
chi0_wk = chi_wk_from_chi_wr(chi0_wr)
del chi0_wr
return chi0_wk
def solve_lattice_bse_depr(g_wk, gamma_wnn, tail_corr_nwf=-1):
fmesh_huge, kmesh = g_wk.mesh.components
bmesh = gamma_wnn.mesh.components[0]
fmesh = gamma_wnn.mesh.components[1]
nk = len(kmesh)
nw = (len(bmesh) + 1) // 2
nwf = len(fmesh) // 2
nwf_sigma = len(fmesh_huge) // 2
if mpi.is_master_node():
print((tprf_banner(), "\n"))
print('Lattcie BSE with local vertex approximation.\n')
print(('nk = ', nk))
print(('nw = ', nw))
print(('nwf = ', nwf))
print(('nwf_sigma = ', nwf_sigma))
print(('nwf = ', tail_corr_nwf, ' (gf)'))
print()
# -- Lattice BSE calc with built in trace using g_wk
from triqs_tprf.lattice import chiq_sum_nu_from_g_wk_and_gamma_PH
chi_kw = chiq_sum_nu_from_g_wk_and_gamma_PH(g_wk,
gamma_wnn,
tail_corr_nwf=tail_corr_nwf)
return chi_kw
def solve_lattice_bse(g_wk, gamma_wnn, tail_corr_nwf=None):
fmesh_g = g_wk.mesh.components[0]
kmesh = g_wk.mesh.components[1]
bmesh = gamma_wnn.mesh.components[0]
fmesh = gamma_wnn.mesh.components[1]
nk = len(kmesh)
nw = (len(bmesh) + 1) / 2
nwf = len(fmesh) / 2
nwf_g = len(fmesh_g) / 2
if mpi.is_master_node():
print tprf_banner(), "\n"
print 'Lattcie BSE with local vertex approximation.\n'
print 'nk =', nk
print 'nw =', nw
print 'nwf =', nwf
print 'nwf_g =', nwf_g
print 'tail_corr_nwf =', tail_corr_nwf
print
if tail_corr_nwf is None:
tail_corr_nwf = nwf
mpi.report('--> chi0_wnk_tail_corr')
chi0_wnk_tail_corr = get_chi0_wnk(g_wk, nw=nw, nwf=tail_corr_nwf)
mpi.report('--> trace chi0_wnk_tail_corr (WARNING! NO TAIL FIT. FIXME!)')
chi0_wk_tail_corr = chi0q_sum_nu_tail_corr_PH(chi0_wnk_tail_corr)
#chi0_wk_tail_corr = chi0q_sum_nu(chi0_wnk_tail_corr)
mpi.barrier()
mpi.report('B1 ' +
str(chi0_wk_tail_corr[Idx(0), Idx(0, 0, 0)][0, 0, 0, 0]))
mpi.barrier()
mpi.report('--> chi0_wnk_tail_corr to chi0_wnk')
if tail_corr_nwf != nwf:
mpi.report('--> fixed_fermionic_window_python_wnk')
chi0_wnk = fixed_fermionic_window_python_wnk(chi0_wnk_tail_corr,
nwf=nwf)
else:
chi0_wnk = chi0_wnk_tail_corr.copy()
del chi0_wnk_tail_corr
mpi.barrier()
mpi.report('C ' + str(chi0_wnk[Idx(0), Idx(0), Idx(0, 0, 0)][0, 0, 0, 0]))
mpi.barrier()
mpi.report('--> trace chi0_wnk')
chi0_wk = chi0q_sum_nu(chi0_wnk)
mpi.barrier()
mpi.report('D ' + str(chi0_wk[Idx(0), Idx(0, 0, 0)][0, 0, 0, 0]))
mpi.barrier()
dchi_wk = chi0_wk_tail_corr - chi0_wk
chi0_kw = Gf(mesh=MeshProduct(kmesh, bmesh),
target_shape=chi0_wk_tail_corr.target_shape)
chi0_kw.data[:] = chi0_wk_tail_corr.data.swapaxes(0, 1)
del chi0_wk
del chi0_wk_tail_corr
assert (chi0_wnk.mesh.components[0] == bmesh)
assert (chi0_wnk.mesh.components[1] == fmesh)
assert (chi0_wnk.mesh.components[2] == kmesh)
# -- Lattice BSE calc with built in trace
mpi.report('--> chi_kw from BSE')
#mpi.report('DEBUG BSE INACTIVE'*72)
chi_kw = chiq_sum_nu_from_chi0q_and_gamma_PH(chi0_wnk, gamma_wnn)
#chi_kw = chi0_kw.copy()
mpi.barrier()
mpi.report('--> chi_kw from BSE (done)')
del chi0_wnk
mpi.report('--> chi_kw tail corrected (using chi0_wnk)')
for k in kmesh:
chi_kw[
k, :] += dchi_wk[:,
k] # -- account for high freq of chi_0 (better than nothing)
del dchi_wk
mpi.report('--> solve_lattice_bse, done.')
return chi_kw, chi0_kw
def solve_lattice_bse(g_wk, gamma_wnn, tail_corr_nwf=None):
r""" Compute the generalized lattice susceptibility
:math:`\chi_{abcd}(\omega, \mathbf{k})` using the Bethe-Salpeter
equation (BSE).
Parameters
----------
g_wk : Single-particle Green's function :math:`G_{ab}(\omega, \mathbf{k})`.
gamma_wnn : Local particle-hole vertex function
:math:`\Gamma_{abcd}(\omega, \nu, \nu')`
tail_corr_nwf : Number of fermionic freqiencies to use in the
tail correction of the sum over fermionic frequencies.
Returns
-------
chi0_wk : Generalized lattice susceptibility
:math:`\chi_{abcd}(\omega, \mathbf{k})`
"""
fmesh_g = g_wk.mesh.components[0]
kmesh = g_wk.mesh.components[1]
bmesh = gamma_wnn.mesh.components[0]
fmesh = gamma_wnn.mesh.components[1]
nk = len(kmesh)
nw = (len(bmesh) + 1) / 2
nwf = len(fmesh) / 2
nwf_g = len(fmesh_g) / 2
if mpi.is_master_node():
print tprf_banner(), "\n"
print 'Lattcie BSE with local vertex approximation.\n'
print 'nk =', nk
print 'nw =', nw
print 'nwf =', nwf
print 'nwf_g =', nwf_g
print 'tail_corr_nwf =', tail_corr_nwf
print
if tail_corr_nwf is None:
tail_corr_nwf = nwf
mpi.report('--> chi0_wnk_tail_corr')
chi0_wnk_tail_corr = get_chi0_wnk(g_wk, nw=nw, nwf=tail_corr_nwf)
mpi.report('--> trace chi0_wnk_tail_corr (WARNING! NO TAIL FIT. FIXME!)')
chi0_wk_tail_corr = chi0q_sum_nu_tail_corr_PH(chi0_wnk_tail_corr)
#chi0_wk_tail_corr = chi0q_sum_nu(chi0_wnk_tail_corr)
mpi.barrier()
mpi.report('B1 ' +
str(chi0_wk_tail_corr[Idx(0), Idx(0, 0, 0)][0, 0, 0, 0]))
mpi.barrier()
mpi.report('--> chi0_wnk_tail_corr to chi0_wnk')
if tail_corr_nwf != nwf:
mpi.report('--> fixed_fermionic_window_python_wnk')
chi0_wnk = fixed_fermionic_window_python_wnk(chi0_wnk_tail_corr,
nwf=nwf)
else:
chi0_wnk = chi0_wnk_tail_corr.copy()
del chi0_wnk_tail_corr
mpi.barrier()
mpi.report('C ' + str(chi0_wnk[Idx(0), Idx(0), Idx(0, 0, 0)][0, 0, 0, 0]))
mpi.barrier()
mpi.report('--> trace chi0_wnk')
chi0_wk = chi0q_sum_nu(chi0_wnk)
mpi.barrier()
mpi.report('D ' + str(chi0_wk[Idx(0), Idx(0, 0, 0)][0, 0, 0, 0]))
mpi.barrier()
dchi_wk = chi0_wk_tail_corr - chi0_wk
chi0_kw = Gf(mesh=MeshProduct(kmesh, bmesh),
target_shape=chi0_wk_tail_corr.target_shape)
chi0_kw.data[:] = chi0_wk_tail_corr.data.swapaxes(0, 1)
del chi0_wk
del chi0_wk_tail_corr
assert (chi0_wnk.mesh.components[0] == bmesh)
assert (chi0_wnk.mesh.components[1] == fmesh)
assert (chi0_wnk.mesh.components[2] == kmesh)
# -- Lattice BSE calc with built in trace
mpi.report('--> chi_kw from BSE')
#mpi.report('DEBUG BSE INACTIVE'*72)
chi_kw = chiq_sum_nu_from_chi0q_and_gamma_PH(chi0_wnk, gamma_wnn)
#chi_kw = chi0_kw.copy()
mpi.barrier()
mpi.report('--> chi_kw from BSE (done)')
del chi0_wnk
mpi.report('--> chi_kw tail corrected (using chi0_wnk)')
for k in kmesh:
chi_kw[
k, :] += dchi_wk[:,
k] # -- account for high freq of chi_0 (better than nothing)
del dchi_wk
mpi.report('--> solve_lattice_bse, done.')
return chi_kw, chi0_kw
def imtime_bubble_chi0_wk(g_wk, nw=1):
ncores = multiprocessing.cpu_count()
wmesh, kmesh = g_wk.mesh.components
norb = g_wk.target_shape[0]
beta = wmesh.beta
nw_g = len(wmesh)
nk = len(kmesh)
ntau = 2 * nw_g
# -- Memory Approximation
ng_tr = ntau * np.prod(nk) * norb**2 # storing G(tau, r)
ng_wr = nw_g * np.prod(nk) * norb**2 # storing G(w, r)
ng_t = ntau * norb**2 # storing G(tau)
nchi_tr = ntau * np.prod(nk) * norb**4 # storing \chi(tau, r)
nchi_wr = nw * np.prod(nk) * norb**4 # storing \chi(w, r)
nchi_t = ntau * norb**4 # storing \chi(tau)
nchi_w = nw * norb**4 # storing \chi(w)
nchi_r = np.prod(nk) * norb**4 # storing \chi(r)
if nw == 1:
ntot_case_1 = ng_tr + ng_wr
ntot_case_2 = ng_tr + nchi_wr + ncores * (nchi_t + 2 * ng_t)
ntot_case_3 = 4 * nchi_wr
ntot = max(ntot_case_1, ntot_case_2, ntot_case_3)
else:
ntot_case_1 = ng_tr + nchi_tr + ncores * (nchi_t + 2 * ng_t)
ntot_case_2 = nchi_tr + nchi_wr + ncores * (nchi_w + nchi_t)
ntot = max(ntot_case_1, ntot_case_2)
nbytes = ntot * np.complex128().nbytes
ngb = nbytes / 1024.**3
if mpi.is_master_node():
print tprf_banner(), "\n"
print 'beta =', beta
print 'nk =', nk
print 'nw =', nw_g
print 'norb =', norb
print
print 'Approx. Memory Utilization: %2.2f GB\n' % ngb
mpi.report('--> fourier_wk_to_wr')
g_wr = fourier_wk_to_wr(g_wk)
del g_wk
mpi.report('--> fourier_wr_to_tr')
g_tr = fourier_wr_to_tr(g_wr)
del g_wr
if nw == 1:
mpi.report('--> chi0_w0r_from_grt_PH (bubble in tau & r)')
chi0_wr = chi0_w0r_from_grt_PH(g_tr)
del g_tr
else:
mpi.report('--> chi0_tr_from_grt_PH (bubble in tau & r)')
chi0_tr = chi0_tr_from_grt_PH(g_tr)
del g_tr
mpi.report('--> chi_wr_from_chi_tr')
chi0_wr = chi_wr_from_chi_tr(chi0_tr, nw=nw)
del chi0_tr
mpi.report('--> chi_wk_from_chi_wr (r->k)')
chi0_wk = chi_wk_from_chi_wr(chi0_wr)
del chi0_wr
return chi0_wk
def solve_lattice_bse_at_specific_w(g_wk, gamma_wnn, nw_index):
r""" Compute the generalized lattice susceptibility
:math:`\chi_{\bar{a}b\bar{c}d}(i\omega_{n=\mathrm{nw\_index}}, \mathbf{k})` using the Bethe-Salpeter
equation (BSE) for a specific :math:`i\omega_{n=\mathrm{nw\_index}}`.
Parameters
----------
g_wk : Gf,
Single-particle Green's function :math:`G_{a\bar{b}}(i\nu_n, \mathbf{k})`.
gamma_wnn : Gf,
Local particle-hole vertex function
:math:`\Gamma_{a\bar{b}c\bar{d}}(i\omega_n, i\nu_n, i\nu_n')`.
nw_index : int,
The bosonic Matsubara frequency index :math:`i\omega_{n=\mathrm{nw\_index}}`
at which the BSE is solved.
Returns
-------
chi_k : Gf,
Generalized lattice susceptibility
:math:`\chi_{\bar{a}b\bar{c}d}(i\omega_{n=\mathrm{nw\_index}}, \mathbf{k})`.
chi0_k : Gf,
Generalized bare lattice susceptibility
:math:`\chi^0_{\bar{a}b\bar{c}d}(i\omega_{n=\mathrm{nw\_index}}, \mathbf{k})`.
"""
# Only use \Gamma at the specific \omega
gamma_nn = gamma_wnn[Idx(nw_index), :, :]
# Keep fake bosonic mesh for usability with other functions
gamma_wnn = add_fake_bosonic_mesh(gamma_nn)
fmesh_g = g_wk.mesh.components[0]
kmesh = g_wk.mesh.components[1]
bmesh = gamma_wnn.mesh.components[0]
fmesh = gamma_wnn.mesh.components[1]
nk = len(kmesh)
nwf = len(fmesh) // 2
nwf_g = len(fmesh_g) // 2
if mpi.is_master_node():
print(tprf_banner(), "\n")
print(
'Lattcie BSE with local vertex approximation at specific \omega.\n'
)
print('nk =', nk)
print('nw_index =', nw_index)
print('nwf =', nwf)
print('nwf_g =', nwf_g)
print()
mpi.report('--> chi0_wk_tail_corr')
# Calculate chi0_wk up to the specific \omega
chi0_wk_tail_corr = imtime_bubble_chi0_wk(g_wk,
nw=np.abs(nw_index) + 1,
save_memory=True)
# Only use specific \omega, but put back on fake bosonic mesh
chi0_k_tail_corr = chi0_wk_tail_corr[Idx(nw_index), :]
chi0_wk_tail_corr = add_fake_bosonic_mesh(chi0_k_tail_corr,
beta=bmesh.beta)
chi0_nk = get_chi0_nk_at_specific_w(g_wk, nw_index=nw_index, nwf=nwf)
# Keep fake bosonic mesh for usability with other functions
chi0_wnk = add_fake_bosonic_mesh(chi0_nk)
mpi.report('--> trace chi0_wnk')
chi0_wk = chi0q_sum_nu(chi0_wnk)
dchi_wk = chi0_wk_tail_corr - chi0_wk
chi0_kw = Gf(mesh=MeshProduct(kmesh, bmesh),
target_shape=chi0_wk_tail_corr.target_shape)
chi0_kw.data[:] = chi0_wk_tail_corr.data.swapaxes(0, 1)
del chi0_wk
del chi0_wk_tail_corr
assert (chi0_wnk.mesh.components[0] == bmesh)
assert (chi0_wnk.mesh.components[1] == fmesh)
assert (chi0_wnk.mesh.components[2] == kmesh)
# -- Lattice BSE calc with built in trace
mpi.report('--> chi_kw from BSE')
#mpi.report('DEBUG BSE INACTIVE'*72)
chi_kw = chiq_sum_nu_from_chi0q_and_gamma_PH(chi0_wnk, gamma_wnn)
#chi_kw = chi0_kw.copy()
mpi.barrier()
mpi.report('--> chi_kw from BSE (done)')
del chi0_wnk
mpi.report('--> chi_kw tail corrected (using chi0_wnk)')
for k in kmesh:
chi_kw[
k, :] += dchi_wk[:,
k] # -- account for high freq of chi_0 (better than nothing)
del dchi_wk
mpi.report('--> solve_lattice_bse, done.')
chi_k = chi_kw[:, Idx(0)]
del chi_kw
chi0_k = chi0_kw[:, Idx(0)]
del chi0_kw
return chi_k, chi0_k
def solve_lattice_bse(g_wk, gamma_wnn):
r""" Compute the generalized lattice susceptibility
:math:`\chi_{\bar{a}b\bar{c}d}(\mathbf{k}, \omega_n)` using the Bethe-Salpeter
equation (BSE).
Parameters
----------
g_wk : Gf,
Single-particle Green's function :math:`G_{a\bar{b}}(i\nu_n, \mathbf{k})`.
gamma_wnn : Gf,
Local particle-hole vertex function
:math:`\Gamma_{a\bar{b}c\bar{d}}(i\omega_n, i\nu_n, i\nu_n')`.
Returns
-------
chi_kw : Gf,
Generalized lattice susceptibility
:math:`\chi_{\bar{a}b\bar{c}d}(\mathbf{k}, i\omega_n)`.
chi0_kw : Gf,
Generalized bare lattice susceptibility
:math:`\chi^0_{\bar{a}b\bar{c}d}(\mathbf{k}, i\omega_n)`.
"""
fmesh_g = g_wk.mesh.components[0]
kmesh = g_wk.mesh.components[1]
bmesh = gamma_wnn.mesh.components[0]
fmesh = gamma_wnn.mesh.components[1]
nk = len(kmesh)
nw = (len(bmesh) + 1) // 2
nwf = len(fmesh) // 2
nwf_g = len(fmesh_g) // 2
if mpi.is_master_node():
print(tprf_banner(), "\n")
print('Lattcie BSE with local vertex approximation.\n')
print('nk =', nk)
print('nw =', nw)
print('nwf =', nwf)
print('nwf_g =', nwf_g)
print()
mpi.report('--> chi0_wk_tail_corr')
chi0_wk_tail_corr = imtime_bubble_chi0_wk(g_wk, nw=nw)
mpi.barrier()
mpi.report('B1 ' +
str(chi0_wk_tail_corr[Idx(0), Idx(0, 0, 0)][0, 0, 0, 0]))
mpi.barrier()
chi0_wnk = get_chi0_wnk(g_wk, nw=nw, nwf=nwf)
mpi.barrier()
mpi.report('C ' + str(chi0_wnk[Idx(0), Idx(0), Idx(0, 0, 0)][0, 0, 0, 0]))
mpi.barrier()
mpi.report('--> trace chi0_wnk')
chi0_wk = chi0q_sum_nu(chi0_wnk)
mpi.barrier()
mpi.report('D ' + str(chi0_wk[Idx(0), Idx(0, 0, 0)][0, 0, 0, 0]))
mpi.barrier()
dchi_wk = chi0_wk_tail_corr - chi0_wk
chi0_kw = Gf(mesh=MeshProduct(kmesh, bmesh),
target_shape=chi0_wk_tail_corr.target_shape)
chi0_kw.data[:] = chi0_wk_tail_corr.data.swapaxes(0, 1)
del chi0_wk
del chi0_wk_tail_corr
assert (chi0_wnk.mesh.components[0] == bmesh)
assert (chi0_wnk.mesh.components[1] == fmesh)
assert (chi0_wnk.mesh.components[2] == kmesh)
# -- Lattice BSE calc with built in trace
mpi.report('--> chi_kw from BSE')
#mpi.report('DEBUG BSE INACTIVE'*72)
chi_kw = chiq_sum_nu_from_chi0q_and_gamma_PH(chi0_wnk, gamma_wnn)
#chi_kw = chi0_kw.copy()
mpi.barrier()
mpi.report('--> chi_kw from BSE (done)')
del chi0_wnk
mpi.report('--> chi_kw tail corrected (using chi0_wnk)')
for k in kmesh:
chi_kw[
k, :] += dchi_wk[:,
k] # -- account for high freq of chi_0 (better than nothing)
del dchi_wk
mpi.report('--> solve_lattice_bse, done.')
return chi_kw, chi0_kw
