def __init__(self, e_k, beta, H_int=None, gf_struct=None,
mu0=0., mu_max=10, mu_min=-10.):
if mpi.is_master_node():
print(self.logo())
gf_struct = fix_gf_struct_type(gf_struct)
self.mu = mu0
self.beta = beta
self.mu_max = mu_max
self.mu_min = mu_min
self.e_k = e_k.copy()
self.e_k_MF = e_k.copy()
self.n_k = len(self.e_k.mesh)
self.target_shape = self.e_k.target_shape
self.shape_ab = self.e_k.target_shape
self.shape_abcd = list(self.shape_ab) * 2
self.norb = self.target_shape[0]
self.triu_idxs = np.triu_indices(self.norb, k=1)
if mpi.is_master_node():
print('beta =', self.beta)
print('mu =', self.mu)
print('bands =', self.norb)
print('n_k =', len(self.e_k.mesh))
print('H_int =', H_int)
print()
if gf_struct is None:
assert( H_int is None ), \
'Error: gf_struct = None, but H_int is not None'
if H_int is not None:
assert( gf_struct is not None ), \
'Error: H_int = None, but gf_struct is not None'
fundamental_operators = fundamental_operators_from_gf_struct(gf_struct)
if mpi.is_master_node():
print('gf_struct =', gf_struct)
print('fundamental_operators =', fundamental_operators)
print()
assert( is_operator_composed_of_only_fundamental_operators(
H_int, fundamental_operators) ), \
'Error: H_int is incompatible with gf_struct and its fundamental_operators'
self.U_abcd = get_rpa_tensor(H_int, fundamental_operators)
else:
self.U_abcd = np.zeros(self.shape_abcd)
def dmft_step(Delta_in):
global itern
itern += 1
if verbose:
print("Iteration %i min_iter=%i max_iter=%i\n" % (itern, min_iter, max_iter))
Delta_in_fixed = fix_hyb_function(Delta_in, Delta_min)
S.Delta_w << Delta_in_fixed
S.solve(**sp) # Solve the impurity model
global Gself, Gloc, Gloc_prev
Gself = calc_G(Delta_in_fixed, S.Sigma_w, mu) # impurity GF ("self-energy-trick" improved)
Gloc, Delta = self_consistency(S.Sigma_w) # apply the DMFT self-consistency equation
diff_loc_imp = gf_diff(Gself, Gloc) # difference between impurity and local lattice GF
diff_prev = gf_diff(Gloc, Gloc_prev) # difference between two consecutively computed local latice GFs
Gloc_prev = Gloc.copy()
occupancy = calc_occupancy(Delta, S.Sigma_w, mu)
diff_occupancy = abs(occupancy-occupancy_goal) # this difference is used as the measure of deviation
stats = OrderedDict([("itern", itern), ("mu", mu), ("diff_loc_imp", diff_loc_imp), ("diff_prev", diff_prev),
("diff_occupancy", diff_occupancy), ("occupancy", occupancy)])
for i in observables:
stats[i] = S.expv[i]
header_string = fmt_str_header(len(stats)).format(*[i for i in stats.keys()])
stats_string = fmt_str(len(stats)).format(*[i for i in stats.values()])
if mpi.is_master_node():
if itern == 1: stats_file.write(header_string)
stats_file.write(stats_string)
if verbose: print("stats: %sstats: %s" % (header_string, stats_string))
if store_steps:
os.mkdir(str(itern)) # one subdirectory per iteration
save_BlockGf(str(itern)+"/Delta", Delta_in_fixed)
save_BlockGf(str(itern)+"/Sigma", S.Sigma_w) # self-energy
save_BlockGf(str(itern)+"/G", Gloc) # local lattice Green's function
save_BlockA(str(itern)+"/A", Gloc) # spectral function of local lattice GF
store_result(str(itern)+"/"+solution_filename, S)
if mpi.is_master_node():
store_result(checkpoint_filename, S) # for checkpoint/restart functionality
# Check for convergence. The only way to exit the DMFT loop is by generating exceptions.
if (diff_loc_imp < eps_loc_imp and
diff_prev < eps_prev and
diff_occupancy < eps_occupancy and
itern >= min_iter):
raise Converged(stats_string)
if (itern == max_iter):
raise FailedToConverge(stats_string)
if occup_method == "adjust":
Gloc, Delta = adjust_mu(Delta, S.Sigma_w) # here we update mu to get closer to target occupancy
return Delta
def __init__(self, param, dmft_param):
self.param = param
self.dmft_param = dmft_param
self.occupancy_goal = param["occupancy"]
self.T = param["T"]
self.observables = [] # List of expectation values to compute
self.cp = {} # Dictinary with creator parameters
self.sp = {
"T": self.T,
"model_parameters": {}
} # Dictionary with solver parameters
self.mp = {} # Dictionary with model parameters
self.nrgp = {
} # Dictionary with low-level NRG Parameters (optional tweaks)
# Open file with basic information (convergence criteria, occupancy, expectation values of operators) for monitoring the iteration process
if mpi.is_master_node():
self.stats_file = open(self.stats_filename, "w",
buffering=1) # line buffered
# Initialize a function ht0 for calculating the Hilbert transform of the DOS
if (param["dos"] == "Bethe"):
self.ht1 = lambda z: 2 * (
z - 1j * np.sign(z.imag) * np.sqrt(1 - z**2)
) # Analytical expression for Hilbert transform of Bethe lattice DOS
self.ht0 = lambda z: self.ht1(z / param["Bethe_unit"])
else:
table = np.loadtxt(param["dos"])
self.dosA = Gf(mesh=MeshReFreqPts(table[:, 0]), target_shape=[])
for i, w in enumerate(self.dosA.mesh):
self.dosA[w] = np.array([[table[i, 1]]])
self.ht0 = lambda z: hilbert_transform_refreq(self.dosA, z)
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 main(input_file, output_file):
"""
Solve the impurity problem.
"""
import time
t_start = time.time()
with HDFArchive(os.path.abspath(input_file), 'r') as h:
rot = h['rot'] if 'rot' in h else None
beta = h['beta']
gf_struct = h['gf_struct']
# convert a dict to a list of pairs [ (str,[int,...]), ...]
gf_struct = [(k, list(v)) for k, v in gf_struct.items()]
u_mat = h['u_mat']
n_iw = h['n_iw']
G0_iw = h['G0_iw']
params = h['params']
if rot is not None:
raise RuntimeError("TRIQS/HubbardI interface does not support basis rotation!")
h_int = make_h_int(u_mat, gf_struct)
# Create a working horse
S = Solver(beta, gf_struct, n_iw)
S.G0_iw << G0_iw
for k in params:
# e.g. numpy.bool_ to bool
params[k] = convert_to_built_in_scalar_type(params[k])
S.solve(h_int=h_int, **params)
# Retrieve results from the working horse
Sigma_iw = S.Sigma_iw.copy()
G_iw = S.G_iw.copy()
if mpi.is_master_node():
with HDFArchive(os.path.abspath(output_file), 'w') as h:
h['Sigma_iw'] = Sigma_iw
h['Gimp_iw'] = G_iw
t_end = time.time()
if mpi.is_master_node():
print('TRIQS/hubbardI ran for {} seconds.'.format(t_end-t_start))
def test_mpi(self):
a = Toto(0)
if mpi.is_master_node():
a = Toto(1)
mpi.bcast(a)
self.assertEqual(a, Toto(1))
class test_SIAM(unittest.TestCase):
# Construct Parameters
cp = {}
cp["model"] = "SIAM"
cp["symtype"] = "QS"
cp["mesh_max"] = 1.0
cp["mesh_min"] = 1e-3
cp["mesh_ratio"] = 1.1
# Set up the Solver
S = Solver(**cp)
# Solve Parameters
sp = {}
sp["T"] = 1e-3
sp["Lambda"] = 4.0
sp["Nz"] = 4
sp["Tmin"] = 1e-4
sp["keep"] = 50
sp["keepenergy"] = 6.0
# Model Parameters
mp = {}
mp["U1"] = 0.5
mp["eps1"] = -0.24
sp["model_parameters"] = mp
# Low-level NRG Parameters
np = {}
np["bins"] = 50
S.set_nrg_params(**np)
# # Initialize hybridization function
S.Delta_w['imp'] << 0.1 * SemiCircular(1.0)
# Solve the impurity model
S.solve(**sp)
if mpi.is_master_node():
# Store the Result
fnout = "MPI_SIAM_QS_np%i.out.h5" % mpi.size
with HDFArchive(fnout, 'w') as arch:
arch["A_w"] = S.A_w
arch["G_w"] = S.G_w
arch["F_w"] = S.F_w
arch["Sigma_w"] = S.Sigma_w
# Compare against reference result
fnref = "MPI_SIAM_QS.ref.h5" # the same for all cases!
h5diff(fnout, fnref)
def is_vasp_running(vasp_pid):
"""
Tests if VASP initial process is still alive.
"""
pid_exists = False
if mpi.is_master_node():
try:
os.kill(vasp_pid, 0)
except OSError as e:
pid_exists = e.errno == errno.EPERM
else:
pid_exists = True
pid_exists = mpi.bcast(pid_exists)
return pid_exists
class test_SIAM(unittest.TestCase):
# Construct Parameters
cp = {}
cp["model"] = "SIAM"
cp["symtype"] = "QS"
cp["mesh_max"] = 1.0
cp["mesh_min"] = 1e-3
cp["mesh_ratio"] = 1.1
# Set up the Solver
S = Solver(**cp)
# Solve Parameters
sp = {}
sp["T"] = 1e-3
sp["Lambda"] = 4.0
sp["Nz"] = 2
sp["Tmin"] = 1e-4
sp["keep"] = 50
sp["keepenergy"] = 6.0
# Model Parameters
mp = {}
mp["U1"] = 0.5
mp["eps1"] = -0.24
sp["model_parameters"] = mp
# Low-level NRG Parameters
np = {}
np["bins"] = 50
S.set_nrg_params(**np)
# # Initialize hybridization function
S.Delta_w['imp'] << 0.1 * SemiCircular(1.0)
# Solve the impurity model
S.solve(**sp)
if mpi.is_master_node(): HDFArchive('Solver.h5', 'w')['S'] = S
# Rerun the Solver and Compare
S_old = HDFArchive('Solver.h5', 'r')['S']
S_old.solve(**S_old.last_solve_params)
assert_block_gfs_are_close(S_old.G_w, S.G_w, 1e-12)
def repack(self):
"""
Calls the h5repack routine in order to reduce the file size of the hdf5 archive.
Note
----
Should only be used before the first invokation of HDFArchive in the program,
otherwise the hdf5 linking will be broken.
"""
import subprocess
if not (mpi.is_master_node()):
return
mpi.report("Repacking the file %s" % self.hdf_file)
retcode = subprocess.call(
["h5repack", "-i%s" % self.hdf_file, "-otemphgfrt.h5"])
if retcode != 0:
mpi.report("h5repack failed!")
else:
subprocess.call(["mv", "-f", "temphgfrt.h5", "%s" % self.hdf_file])
def is_vasp_lock_present():
res_bool = False
if mpi.is_master_node():
res_bool = os.path.isfile('./vasp.lock')
res_bool = mpi.bcast(res_bool)
return res_bool
def run_all(vasp_pid, dmft_cycle, cfg_file, n_iter, n_iter_dft, vasp_version):
"""
"""
mpi.report(" Waiting for VASP lock to appear...")
while not is_vasp_lock_present():
time.sleep(1)
vasp_running = True
iter = 0
while vasp_running:
if debug: print(bcolors.RED + "rank %s" % (mpi.rank) + bcolors.ENDC)
mpi.report(" Waiting for VASP lock to disappear...")
mpi.barrier()
while is_vasp_lock_present():
time.sleep(1)
# if debug: print bcolors.YELLOW + " waiting: rank %s"%(mpi.rank) + bcolors.ENDC
if not is_vasp_running(vasp_pid):
mpi.report(" VASP stopped")
vasp_running = False
break
# Tell VASP to stop if the maximum number of iterations is reached
if debug:
print(bcolors.MAGENTA + "rank %s" % (mpi.rank) + bcolors.ENDC)
err = 0
exc = None
if debug:
print(bcolors.BLUE + "plovasp: rank %s" % (mpi.rank) +
bcolors.ENDC)
if mpi.is_master_node():
converter.generate_and_output_as_text(cfg_file, vasp_dir='./')
# Read energy from OSZICAR
dft_energy = get_dft_energy()
mpi.barrier()
if debug: print(bcolors.GREEN + "rank %s" % (mpi.rank) + bcolors.ENDC)
corr_energy, dft_dc = dmft_cycle()
mpi.barrier()
if mpi.is_master_node():
total_energy = dft_energy + corr_energy - dft_dc
print()
print("=" * 80)
print(" Total energy: ", total_energy)
print(" DFT energy: ", dft_energy)
print(" Corr. energy: ", corr_energy)
print(" DFT DC: ", dft_dc)
print("=" * 80)
print()
# check if we should do additional VASP calculations
# in the standard VASP version, VASP writes out GAMMA itself
# so that if we want to keep GAMMA fixed we have to copy it to
# GAMMA_recent and copy it back after VASP has completed an iteration
# if we are using a hacked Version of VASP where the write out is
# disabled we can skip this step.
# the hack consists of removing the call of LPRJ_LDApU in VASP src file
# electron.F around line 644
iter_dft = 0
if vasp_version == 'standard':
copyfile(src='GAMMA', dst='GAMMA_recent')
while iter_dft < n_iter_dft:
if mpi.is_master_node():
open('./vasp.lock', 'a').close()
while is_vasp_lock_present():
time.sleep(1)
if not is_vasp_running(vasp_pid):
mpi.report(" VASP stopped")
vasp_running = False
break
iter_dft += 1
if vasp_version == 'standard':
copyfile(src='GAMMA_recent', dst='GAMMA')
iter += 1
if iter == n_iter:
print("\n Maximum number of iterations reached.")
print(" Aborting VASP iterations...\n")
f_stop = open('STOPCAR', 'wt')
f_stop.write("LABORT = .TRUE.\n")
f_stop.close()
if mpi.is_master_node():
total_energy = dft_energy + corr_energy - dft_dc
with open('TOTENERGY', 'w') as f:
f.write(" Total energy: %s\n" % (total_energy))
f.write(" DFT energy: %s\n" % (dft_energy))
f.write(" Corr. energy: %s\n" % (corr_energy))
f.write(" DFT DC: %s\n" % (dft_dc))
f.write(" Energy correction: %s\n" % (corr_energy - dft_dc))
mpi.report("***Done")
def main():
import importlib
try:
vasp_pid = int(sys.argv[1])
except (ValueError, KeyError):
if mpi.is_master_node():
print(
"ERROR: VASP process pid must be provided as the first argument"
)
raise
try:
n_iter = int(sys.argv[2])
except (ValueError, KeyError):
if mpi.is_master_node():
print(
"ERROR: Number of iterations must be provided as the second argument"
)
raise
try:
n_iter_dft = int(sys.argv[3])
except (ValueError, KeyError):
if mpi.is_master_node():
print(
"ERROR: Number of VASP iterations with fixed charge density must be provided as the third argument"
)
raise
try:
dmft_script = re.sub("\.py$", "", sys.argv[4])
except:
if mpi.is_master_node():
print(
"ERROR: User-defined DMFT script must be provided as the fourth argument"
)
raise
# Optional parameter: config-file name
try:
cfg_file = sys.argv[5]
except KeyError:
cfg_file = 'plo.cfg'
try:
vasp_version = sys.argv[6]
except KeyError:
vasp_version = 'standard'
if vasp_version != 'standard' and vasp_version != 'no_gamma_write':
raise Exception('vasp_version has to be standard or no_gamma_write')
# if len(sys.argv) > 1:
# vasp_path = sys.argv[1]
# else:
# try:
# vasp_path = os.environ['VASP_DIR']
# except KeyError:
# if mpi.is_master_node():
# print "Path to VASP must be specified either as an argument of in VASP_DIR"
# raise
signal.signal(signal.SIGINT, sigint_handler)
dmft_mod = importlib.import_module(dmft_script)
run_all(vasp_pid, dmft_mod.dmft_cycle, cfg_file, n_iter, n_iter_dft,
vasp_version)
p["n_warmup_cycles"] = 100000
p["n_cycles"] = 1000000
p["perform_tail_fit"] = True
p["fit_max_moment"] = 4
p["fit_min_n"] = 30
p["fit_max_n"] = 60
# If conversion step was not done, we could do it here. Uncomment the lines it you want to do this.
#from triqs_dft_tools.converters.wien2k import *
#Converter = Wien2kConverter(filename=dft_filename, repacking=True)
#Converter.convert_dft_input()
#mpi.barrier()
previous_runs = 0
previous_present = False
if mpi.is_master_node():
with HDFArchive(dft_filename + '.h5', 'a') as f:
if 'dmft_output' in f:
ar = f['dmft_output']
if 'iterations' in ar:
previous_present = True
previous_runs = ar['iterations']
else:
f.create_group('dmft_output')
previous_runs = mpi.bcast(previous_runs)
previous_present = mpi.bcast(previous_present)
SK = SumkDFT(hdf_file=dft_filename + '.h5',
use_dft_blocks=use_blocks,
h_field=h_field)
def convert_dft_input(self,
first_real_part_matrix=True,
only_upper_triangle=False,
weights_in_file=False):
"""
Reads the appropriate files and stores the data for the dft_subgrp in the hdf5 archive.
Parameters
----------
first_real_part_matrix : boolean, optional
Should all the real components for given k be read in first, followed by the imaginary parts?
only_upper_triangle : boolean, optional
Should only the upper triangular part of H(k) be read in?
weights_in_file : boolean, optional
Are the k-point weights to be read in?
"""
# Read and write only on the master node
if not (mpi.is_master_node()):
return
mpi.report("Reading input from %s..." % self.dft_file)
# R is a generator : each R.Next() will return the next number in the
# file
R = ConverterTools.read_fortran_file(self, self.dft_file,
self.fortran_to_replace)
try:
# the energy conversion factor is 1.0, we assume eV in files
energy_unit = 1.0
# read the number of k points
n_k = int(next(R))
k_dep_projection = 0
SP = 0 # no spin-polarision
SO = 0 # no spin-orbit
# total charge below energy window is set to 0
charge_below = 0.0
# density required, for setting the chemical potential
density_required = next(R)
symm_op = 0 # No symmetry groups for the k-sum
# the information on the non-correlated shells is needed for
# defining dimension of matrices:
# number of shells considered in the Wanniers
n_shells = int(next(R))
# corresponds to index R in formulas
# now read the information about the shells (atom, sort, l, dim):
shell_entries = ['atom', 'sort', 'l', 'dim']
shells = [{name: int(val)
for name, val in zip(shell_entries, R)}
for ish in range(n_shells)]
# number of corr. shells (e.g. Fe d, Ce f) in the unit cell,
n_corr_shells = int(next(R))
# corresponds to index R in formulas
# now read the information about the shells (atom, sort, l, dim, SO
# flag, irep):
corr_shell_entries = ['atom', 'sort', 'l', 'dim', 'SO', 'irep']
corr_shells = [{
name: int(val)
for name, val in zip(corr_shell_entries, R)
} for icrsh in range(n_corr_shells)]
# determine the number of inequivalent correlated shells and maps,
# needed for further reading
[n_inequiv_shells, corr_to_inequiv, inequiv_to_corr
] = ConverterTools.det_shell_equivalence(self, corr_shells)
use_rotations = 0
rot_mat = [
numpy.identity(corr_shells[icrsh]['dim'], numpy.complex_)
for icrsh in range(n_corr_shells)
]
rot_mat_time_inv = [0 for i in range(n_corr_shells)]
# Representative representations are read from file
n_reps = [1 for i in range(n_inequiv_shells)]
dim_reps = [0 for i in range(n_inequiv_shells)]
T = []
for ish in range(n_inequiv_shells):
# number of representatives ("subsets"), e.g. t2g and eg
n_reps[ish] = int(next(R))
dim_reps[ish] = [int(next(R)) for i in range(n_reps[ish])
] # dimensions of the subsets
# The transformation matrix:
# is of dimension 2l+1, it is taken to be standard d (as in
# Wien2k)
ll = 2 * corr_shells[inequiv_to_corr[ish]]['l'] + 1
lmax = ll * (corr_shells[inequiv_to_corr[ish]]['SO'] + 1)
T.append(numpy.zeros([lmax, lmax], numpy.complex_))
T[ish] = numpy.array(
[[0.0, 0.0, 1.0, 0.0, 0.0],
[1.0 / sqrt(2.0), 0.0, 0.0, 0.0, 1.0 / sqrt(2.0)],
[-1.0 / sqrt(2.0), 0.0, 0.0, 0.0, 1.0 / sqrt(2.0)],
[0.0, 1.0 / sqrt(2.0), 0.0, -1.0 / sqrt(2.0), 0.0],
[0.0, 1.0 / sqrt(2.0), 0.0, 1.0 / sqrt(2.0), 0.0]])
# Spin blocks to be read:
# number of spins to read for Norbs and Ham, NOT Projectors
n_spin_blocs = SP + 1 - SO
# define the number of n_orbitals for all k points: it is the
# number of total bands and independent of k!
n_orbitals = numpy.ones([n_k, n_spin_blocs], numpy.int) * sum(
[sh['dim'] for sh in shells])
# Initialise the projectors:
proj_mat = numpy.zeros([
n_k, n_spin_blocs, n_corr_shells,
max([crsh['dim'] for crsh in corr_shells]),
numpy.max(n_orbitals)
], numpy.complex_)
# Read the projectors from the file:
for ik in range(n_k):
for icrsh in range(n_corr_shells):
for isp in range(n_spin_blocs):
# calculate the offset:
offset = 0
n_orb = 0
for ish in range(n_shells):
if (n_orb == 0):
if (shells[ish]['atom']
== corr_shells[icrsh]['atom']) and (
shells[ish]['sort']
== corr_shells[icrsh]['sort']):
n_orb = corr_shells[icrsh]['dim']
else:
offset += shells[ish]['dim']
proj_mat[ik, isp, icrsh, 0:n_orb,
offset:offset + n_orb] = numpy.identity(n_orb)
# now define the arrays for weights and hopping ...
# w(k_index), default normalisation
bz_weights = numpy.ones([n_k], numpy.float_) / float(n_k)
hopping = numpy.zeros([
n_k, n_spin_blocs,
numpy.max(n_orbitals),
numpy.max(n_orbitals)
], numpy.complex_)
if (weights_in_file):
# weights in the file
for ik in range(n_k):
bz_weights[ik] = next(R)
# if the sum over spins is in the weights, take it out again!!
sm = sum(bz_weights)
bz_weights[:] /= sm
# Grab the H
for isp in range(n_spin_blocs):
for ik in range(n_k):
n_orb = n_orbitals[ik, isp]
# first read all real components for given k, then read
# imaginary parts
if (first_real_part_matrix):
for i in range(n_orb):
if (only_upper_triangle):
istart = i
else:
istart = 0
for j in range(istart, n_orb):
hopping[ik, isp, i, j] = next(R)
for i in range(n_orb):
if (only_upper_triangle):
istart = i
else:
istart = 0
for j in range(istart, n_orb):
hopping[ik, isp, i, j] += next(R) * 1j
if ((only_upper_triangle) and (i != j)):
hopping[ik, isp, j,
i] = hopping[ik, isp, i,
j].conjugate()
else: # read (real,im) tuple
for i in range(n_orb):
if (only_upper_triangle):
istart = i
else:
istart = 0
for j in range(istart, n_orb):
hopping[ik, isp, i, j] = next(R)
hopping[ik, isp, i, j] += next(R) * 1j
if ((only_upper_triangle) and (i != j)):
hopping[ik, isp, j,
i] = hopping[ik, isp, i,
j].conjugate()
# keep some things that we need for reading parproj:
things_to_set = [
'n_shells', 'shells', 'n_corr_shells', 'corr_shells',
'n_spin_blocs', 'n_orbitals', 'n_k', 'SO', 'SP', 'energy_unit'
]
for it in things_to_set:
setattr(self, it, locals()[it])
except StopIteration: # a more explicit error if the file is corrupted.
raise "HK Converter : reading file dft_file failed!"
R.close()
# Save to the HDF5:
with HDFArchive(self.hdf_file, 'a') as ar:
if not (self.dft_subgrp in ar):
ar.create_group(self.dft_subgrp)
things_to_save = [
'energy_unit', 'n_k', 'k_dep_projection', 'SP', 'SO',
'charge_below', 'density_required', 'symm_op', 'n_shells',
'shells', 'n_corr_shells', 'corr_shells', 'use_rotations',
'rot_mat', 'rot_mat_time_inv', 'n_reps', 'dim_reps', 'T',
'n_orbitals', 'proj_mat', 'bz_weights', 'hopping',
'n_inequiv_shells', 'corr_to_inequiv', 'inequiv_to_corr'
]
for it in things_to_save:
ar[self.dft_subgrp][it] = locals()[it]
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
def is_master_node():
if is_mpi_loaded():
import triqs.utility.mpi as mpi
return mpi.is_master_node()
else:
return True
beta = 100.0
# We analyze the block structure of the Hamiltonian
Sigma = SK_tools.block_structure.create_gf(beta=beta)
SK_tools.put_Sigma([Sigma])
G = SK_tools.extract_G_loc()
SK_tools.analyse_block_structure_from_gf(G, threshold = 1e-2)
gf_struct = SK_tools.gf_struct_solver[0]
S = Solver(beta=beta, gf_struct=gf_struct)
# non-interacting chemical potential
chemical_potential0 = 0.0
if mpi.is_master_node():
ar = HDFArchive(filename+'.h5','a')
if 'iteration_count' in ar['DMFT_results']:
previous_present = True
iteration_offset = ar['DMFT_results']['iteration_count']+1
print('reading iteration'+str(iteration_offset))
SK_tools.dc_imp = ar['DMFT_results']['Iterations']['dc_imp'+str(iteration_offset-1)]
S.Sigma_w = ar['DMFT_results']['Iterations']['Sigma_w_it'+str(iteration_offset-1)]
dc_energ = ar['DMFT_results']['Iterations']['dc_energ'+str(iteration_offset-1)]
SK_tools.chemical_potential = ar['DMFT_results']['Iterations']['chemical_potential'+str(iteration_offset-1)].real
chemical_potential0 = ar['DMFT_results']['Iterations']['chemical_potential0'].real
mpi.barrier()
S.Sigma_w << mpi.bcast(S.Sigma_w)
SK_tools.chemical_potential = mpi.bcast(SK_tools.chemical_potential)
chemical_potential0 = mpi.bcast(chemical_potential0)
def run_test(t1, filename):
dptkeys = [
'verbosity', 'calculate_sigma', 'calculate_sigma1', 'calculate_sigma2'
]
parms = {
# Solver parameters
'n_iw': 100,
# Physical parameters
'U': 0.5,
't1': t1,
'beta': 10,
# DMFT loop control parameters
'calculate_sigma': True,
'calculate_sigma1': True,
'calculate_sigma2': True,
'measure_G2_iw_ph': True,
"measure_G2_n_bosonic": 10,
"measure_G2_n_fermionic": 10,
"verbosity": 4,
}
parms["N_x"] = 2
parms["N_y"] = 1
parms["N_z"] = 1
parms["ksi_delta"] = 1.0
# Chemical potential depends on the definition of H(k) that is used
parms['chemical_potential_bare'] = 0.
parms['chemical_potential'] = parms['U'] / 2. + parms[
'chemical_potential_bare']
n_orbs = 1 # Number of orbitals
off_diag = True
spin_names = ['up', 'dn'] # Outer (non-hybridizing) blocks
orb_names = ['%s' % i for i in range(n_orbs)] # Orbital indices
gf_struct = op.set_operator_structure(spin_names,
orb_names,
off_diag=off_diag)
if haspomerol:
#####
#
# Reference: 4 site cluster, calculate only G, not G2
#
#####
def calc_reference():
ref_orbs = [
'%s' % i for i in range(n_orbs * parms['N_x'] * parms['N_y'])
]
ref_gf_struct = op.set_operator_structure(spin_names,
ref_orbs,
off_diag=off_diag)
ref_index_converter = {(sn, o): ("loc", int(o),
"down" if sn == "dn" else "up")
for sn, o in product(spin_names, ref_orbs)}
#print ref_index_converter,ref_orbs
ref_ed = PomerolED(ref_index_converter, verbose=True)
ref_N = sum(
ops.n(sn, o) for sn, o in product(spin_names, ref_orbs))
# 2 3
# 0 1
ref_H = (parms["U"] * (ops.n('up', '0') * ops.n('dn', '0') +
ops.n('up', '1') * ops.n('dn', '1')) -
2. * parms['t1'] *
(ops.c_dag('up', '0') * ops.c('up', '1') +
ops.c_dag('up', '1') * ops.c('up', '0') +
ops.c_dag('dn', '0') * ops.c('dn', '1') +
ops.c_dag('dn', '1') * ops.c('dn', '0')) -
parms['chemical_potential'] * ref_N)
# Run the solver
ref_ed.diagonalize(ref_H)
# Compute G(i\omega)
ref_G_iw = ref_ed.G_iw(ref_gf_struct, parms['beta'], parms['n_iw'])
return ref_G_iw
ref_G_iw = calc_reference()
ref = ref_G_iw[ref_spin]
g2_blocks = set([("up", "up"), ("up", "dn"), ("dn", "up"),
("dn", "dn")])
index_converter = {(sn, o):
("loc", int(o), "down" if sn == "dn" else "up")
for sn, o in product(spin_names, orb_names)}
# 1 Bath degree of freedom
# Level of the bath sites
epsilon = [
-parms['chemical_potential_bare'],
]
index_converter.update({
("B%i_%s" % (k, sn), 0):
("bath" + str(k), 0, "down" if sn == "dn" else "up")
for k, sn in product(range(len(epsilon)), spin_names)
})
# Make PomerolED solver object
ed = PomerolED(index_converter, verbose=True)
N = sum(ops.n(sn, o) for sn, o in product(spin_names, orb_names))
H_loc = (parms["U"] * (ops.n('up', '0') * ops.n('dn', '0')) -
parms['chemical_potential'] * N)
# Bath Hamiltonian: levels
H_bath = sum(eps * ops.n("B%i_%s" % (k, sn), 0)
for sn, (k,
eps) in product(spin_names, enumerate(epsilon)))
# Hybridization Hamiltonian
# Bath-impurity hybridization
V = [
-2 * bath_prefactor * t1,
]
H_hyb = ops.Operator()
for k, v in enumerate(V):
H_hyb += sum(
v * ops.c_dag("B%i_%s" % (k, sn), 0) * ops.c(sn, '0') +
np.conj(v) * ops.c_dag(sn, '0') * ops.c("B%i_%s" % (k, sn), 0)
for sn in spin_names)
# Obtain bath sites from Delta and create H_ED
H_ED = H_loc + H_bath + H_hyb
# Run the solver
ed.diagonalize(H_ED)
# Compute G(i\omega)
G_iw = ed.G_iw(gf_struct, parms['beta'], parms['n_iw'])
if parms["measure_G2_iw_ph"]:
common_g2_params = {
'gf_struct': gf_struct,
'beta': parms['beta'],
'blocks': g2_blocks,
'n_iw': parms['measure_G2_n_bosonic']
}
G2_iw = ed.G2_iw_inu_inup(channel="PH",
block_order="AABB",
n_inu=parms['measure_G2_n_fermionic'],
**common_g2_params)
if mpi.is_master_node():
with ar.HDFArchive(filename, 'w') as arch:
arch["parms"] = parms
arch["G_iw"] = G_iw
arch["G2_iw"] = G2_iw
arch["ref"] = ref
else: # haspomerol is False
with ar.HDFArchive(filename, 'r') as arch:
ref = arch['ref']
G_iw = arch['G_iw']
G2_iw = arch['G2_iw']
BL = lattice.BravaisLattice(units=[
(1, 0, 0),
]) #linear lattice
kmesh = gf.MeshBrillouinZone(lattice.BrillouinZone(BL), parms["N_x"])
Hk_blocks = [gf.Gf(indices=orb_names, mesh=kmesh) for spin in spin_names]
Hk = gf.BlockGf(name_list=spin_names, block_list=Hk_blocks)
def Hk_f(k):
return -2 * parms['t1'] * (np.cos(k[0])) * np.eye(1)
for spin, _ in Hk:
for k in Hk.mesh:
Hk[spin][k] = Hk_f(k.value)
# Construct the DF2 program
X = dualfermion.Dpt(beta=parms['beta'],
gf_struct=gf_struct,
Hk=Hk,
n_iw=parms['n_iw'],
n_iw2=parms["measure_G2_n_fermionic"],
n_iW=parms["measure_G2_n_bosonic"])
for name, g0 in X.Delta:
X.Delta[name] << gf.inverse(
gf.iOmega_n +
parms['chemical_potential_bare']) * bath_prefactor**2 * 4 * t1**2
X.G2_iw << G2_iw
# Run the dual perturbation theory
X.gimp << G_iw # Load G from impurity solver
dpt_parms = {key: parms[key] for key in parms if key in dptkeys}
X.run(**dpt_parms)
for o1 in orb_names:
if h_loc_0_offidag:
for o2 in orb_names:
Hloc_0 += atomic_levels[spin][o1, o2] * (
c_dag(spin, o1) * c(spin, o2) +
c_dag(spin, o2) * c(spin, o1))
else:
o2 = o1
Hloc_0 += atomic_levels[spin][o1, o2] * (
c_dag(spin, o1) * c(spin, o2) +
c_dag(spin, o2) * c(spin, o1))
Hloc_0 += (-mu) * N
# store data obtained
if store_h5 and mpi.is_master_node():
with HDFArchive(store_h5_file, 'a') as ar:
ar['block_structure'] = sum_k.block_structure
ar['mu'] = sum_k.chemical_potential
# ar['Gloc'] = Gloc
ar['Hloc_0'] = Hloc_0
# construct interaction matrix
if not 'Hint' in locals():
if h_int_type == 'slater':
mpi.report('setting up slater Hamiltonian')
Umat_full = U_matrix(l=2, U_int=U, J_hund=J, basis='cubic')
# rotate to den mat diag basis
Umat_full_rotated = transform_U_matrix(Umat_full, sum_k.rot_mat[0].T)
def main(input_file, output_file):
"""
Solve the impurity problem.
"""
import time
t_start = time.time()
with HDFArchive(os.path.abspath(input_file), 'r') as h:
rot = h['rot'] if 'rot' in h else None
beta = h['beta']
gf_struct = h['gf_struct']
# convert a dict to a list of pairs [ (str,[int,...]), ...]
gf_struct = [(k, list(v)) for k, v in gf_struct.items()]
u_mat = h['u_mat']
n_iw = h['n_iw']
G0_iw = h['G0_iw']
params = h['params']
use_spin_orbit = len(gf_struct) == 1
# Rotate basis
u_mat_rot = u_mat.copy()
G0_iw_rot = G0_iw.copy()
if not rot is None:
u_mat_rot = rotate_basis(rot,
use_spin_orbit,
u_mat_rot,
Gfs=[G0_iw_rot],
direction='forward')
h_int = make_h_int(u_mat_rot, gf_struct)
# Create a working horse
S = TRIQSCTHYBSolver(beta, gf_struct, n_iw)
S.G0_iw << G0_iw_rot
if 'random_seed' in params:
raise RuntimeError("Do not set random_seed for triqs/cthyb manually")
params['random_seed'] = 34788 + 928374 * mpi.rank + params[
'random_seed_offset']
del params['random_seed_offset']
for k in params:
# e.g. numpy.bool_ to bool
params[k] = convert_to_built_in_scalar_type(params[k])
S.solve(h_int=h_int, **params)
# Retrieve results from the working horse
Sigma_iw = S.Sigma_iw.copy()
G_iw = S.G_iw.copy()
if not rot is None:
Gfs = [Sigma_iw, G_iw]
rotate_basis(rot,
use_spin_orbit,
u_matrix=None,
Gfs=Gfs,
direction='backward')
if mpi.is_master_node():
with HDFArchive(os.path.abspath(output_file), 'w') as h:
h['Sigma_iw'] = Sigma_iw
h['Gimp_iw'] = G_iw
t_end = time.time()
if mpi.is_master_node():
print('TRIQS/cthyb ran for {} seconds.'.format(t_end - t_start))
def dmft_cycle():
filename = 'nio'
Converter = VaspConverter(filename=filename)
Converter.convert_dft_input()
SK = SumkDFT(hdf_file = filename+'.h5', use_dft_blocks = False)
beta = 5.0
Sigma = SK.block_structure.create_gf(beta=beta)
SK.put_Sigma([Sigma])
G = SK.extract_G_loc()
SK.analyse_block_structure_from_gf(G, threshold = 1e-2)
for i_sh in range(len(SK.deg_shells)):
num_block_deg_orbs = len(SK.deg_shells[i_sh])
mpi.report('found {0:d} blocks of degenerate orbitals in shell {1:d}'.format(num_block_deg_orbs, i_sh))
for iblock in range(num_block_deg_orbs):
mpi.report('block {0:d} consists of orbitals:'.format(iblock))
for keys in list(SK.deg_shells[i_sh][iblock].keys()):
mpi.report(' '+keys)
# Setup CTQMC Solver
n_orb = SK.corr_shells[0]['dim']
spin_names = ['up','down']
orb_names = [i for i in range(0,n_orb)]
#gf_struct = set_operator_structure(spin_names, orb_names, orb_hyb)
gf_struct = SK.gf_struct_solver[0]
mpi.report('Sumk to Solver: %s'%SK.sumk_to_solver)
mpi.report('GF struct sumk: %s'%SK.gf_struct_sumk)
mpi.report('GF struct solver: %s'%SK.gf_struct_solver)
S = Solver(beta=beta, gf_struct=gf_struct)
# Construct the Hamiltonian and save it in Hamiltonian_store.txt
H = Operator()
U = 8.0
J = 1.0
U_sph = U_matrix(l=2, U_int=U, J_hund=J)
U_cubic = transform_U_matrix(U_sph, spherical_to_cubic(l=2, convention=''))
Umat, Upmat = reduce_4index_to_2index(U_cubic)
H = h_int_density(spin_names, orb_names, map_operator_structure=SK.sumk_to_solver[0], U=Umat, Uprime=Upmat)
# Print some information on the master node
mpi.report('Greens function structure is: %s '%gf_struct)
mpi.report('U Matrix set to:\n%s'%Umat)
mpi.report('Up Matrix set to:\n%s'%Upmat)
# Parameters for the CTQMC Solver
p = {}
p["max_time"] = -1
p["random_name"] = ""
p["random_seed"] = 123 * mpi.rank + 567
p["length_cycle"] = 100
p["n_warmup_cycles"] = 2000
p["n_cycles"] = 20000
p["fit_max_moment"] = 4
p["fit_min_n"] = 30
p["fit_max_n"] = 50
p["perform_tail_fit"] = True
# Double Counting: 0 FLL, 1 Held, 2 AMF
DC_type = 0
DC_value = 59.0
# Prepare hdf file and and check for previous iterations
n_iterations = 1
iteration_offset = 0
if mpi.is_master_node():
ar = HDFArchive(filename+'.h5','a')
if not 'DMFT_results' in ar: ar.create_group('DMFT_results')
if not 'Iterations' in ar['DMFT_results']: ar['DMFT_results'].create_group('Iterations')
if not 'DMFT_input' in ar: ar.create_group('DMFT_input')
if not 'Iterations' in ar['DMFT_input']: ar['DMFT_input'].create_group('Iterations')
if not 'code_versions' in ar['DMFT_input']: ar['DMFT_input'].create_group('code_versio\
ns')
ar['DMFT_input']['code_versions']["triqs_version"] = triqs_version.version
ar['DMFT_input']['code_versions']["triqs_git"] = triqs_version.git_hash
ar['DMFT_input']['code_versions']["cthyb_version"] = cthyb_version.version
ar['DMFT_input']['code_versions']["cthyb_git"] = cthyb_version.triqs_cthyb_hash
ar['DMFT_input']['code_versions']["dft_tools_version"] = dft_tools_version.version
ar['DMFT_input']['code_versions']["dft_tools_git"] = dft_tools_version.triqs_dft_tools_hash
if 'iteration_count' in ar['DMFT_results']:
iteration_offset = ar['DMFT_results']['iteration_count']+1
S.Sigma_iw = ar['DMFT_results']['Iterations']['Sigma_it'+str(iteration_offset-1)]
SK.dc_imp = ar['DMFT_results']['Iterations']['dc_imp'+str(iteration_offset-1)]
SK.dc_energ = ar['DMFT_results']['Iterations']['dc_energ'+str(iteration_offset-1)]
SK.chemical_potential = ar['DMFT_results']['Iterations']['chemical_potential'+str(iteration_offset-1)].real
ar['DMFT_input']["dmft_script_it"+str(iteration_offset)] = open(sys.argv[0]).read()
iteration_offset = mpi.bcast(iteration_offset)
S.Sigma_iw = mpi.bcast(S.Sigma_iw)
SK.dc_imp = mpi.bcast(SK.dc_imp)
SK.dc_energ = mpi.bcast(SK.dc_energ)
SK.chemical_potential = mpi.bcast(SK.chemical_potential)
# Calc the first G0
SK.symm_deg_gf(S.Sigma_iw, ish=0)
SK.put_Sigma(Sigma_imp = [S.Sigma_iw])
SK.calc_mu(precision=0.01)
S.G_iw << SK.extract_G_loc()[0]
SK.symm_deg_gf(S.G_iw, ish=0)
#Init the DC term and the self-energy if no previous iteration was found
if iteration_offset == 0:
dm = S.G_iw.density()
SK.calc_dc(dm, U_interact=U, J_hund=J, orb=0, use_dc_formula=DC_type,use_dc_value=DC_value)
S.Sigma_iw << SK.dc_imp[0]['up'][0,0]
mpi.report('%s DMFT cycles requested. Starting with iteration %s.'%(n_iterations,iteration_offset))
# The infamous DMFT self consistency cycle
for it in range(iteration_offset, iteration_offset + n_iterations):
mpi.report('Doing iteration: %s'%it)
# Get G0
S.G0_iw << inverse(S.Sigma_iw + inverse(S.G_iw))
# Solve the impurity problem
S.solve(h_int = H, **p)
if mpi.is_master_node():
ar['DMFT_input']['Iterations']['solver_dict_it'+str(it)] = p
ar['DMFT_results']['Iterations']['Gimp_it'+str(it)] = S.G_iw
ar['DMFT_results']['Iterations']['Gtau_it'+str(it)] = S.G_tau
ar['DMFT_results']['Iterations']['Sigma_uns_it'+str(it)] = S.Sigma_iw
# Calculate double counting
dm = S.G_iw.density()
SK.calc_dc(dm, U_interact=U, J_hund=J, orb=0, use_dc_formula=DC_type,use_dc_value=DC_value)
# Get new G
SK.symm_deg_gf(S.Sigma_iw, ish=0)
SK.put_Sigma(Sigma_imp=[S.Sigma_iw])
SK.calc_mu(precision=0.01)
S.G_iw << SK.extract_G_loc()[0]
# print densities
for sig,gf in S.G_iw:
mpi.report("Orbital %s density: %.6f"%(sig,dm[sig][0,0]))
mpi.report('Total charge of Gloc : %.6f'%S.G_iw.total_density())
if mpi.is_master_node():
ar['DMFT_results']['iteration_count'] = it
ar['DMFT_results']['Iterations']['Sigma_it'+str(it)] = S.Sigma_iw
ar['DMFT_results']['Iterations']['Gloc_it'+str(it)] = S.G_iw
ar['DMFT_results']['Iterations']['G0loc_it'+str(it)] = S.G0_iw
ar['DMFT_results']['Iterations']['dc_imp'+str(it)] = SK.dc_imp
ar['DMFT_results']['Iterations']['dc_energ'+str(it)] = SK.dc_energ
ar['DMFT_results']['Iterations']['chemical_potential'+str(it)] = SK.chemical_potential
if mpi.is_master_node():
print('calculating mu...')
SK.chemical_potential = SK.calc_mu( precision = 0.000001 )
if mpi.is_master_node():
print('calculating GAMMA')
SK.calc_density_correction(dm_type='vasp')
if mpi.is_master_node():
print('calculating energy corrections')
correnerg = 0.5 * (S.G_iw * S.Sigma_iw).total_density()
dm = S.G_iw.density() # compute the density matrix of the impurity problem
SK.calc_dc(dm, U_interact=U, J_hund=J, orb=0, use_dc_formula=DC_type,use_dc_value=DC_value)
dc_energ = SK.dc_energ[0]
if mpi.is_master_node():
ar['DMFT_results']['Iterations']['corr_energy_it'+str(it)] = correnerg
ar['DMFT_results']['Iterations']['dc_energy_it'+str(it)] = dc_energ
if mpi.is_master_node(): del ar
return correnerg, dc_energ
Delta_min = 1e-5 # minimal value for the hybridisation function; if too large, it produces incorrect spectral distribution,
# if too small, it leads to discretization problems (1e-5 is usually a good and rather safe choice)
normalize_to_one = True # scaling of the spectral function (relevant in the case of block structure and/or matrix structure of GF)
solution_filename = "solution.h5"
checkpoint_filename = "checkpoint.h5"
# Additional quantities of interest
observables = ["n_d", "n_d^2"]
if B is not None:
observables.extend(["SZd"])
if "Holstein" in model:
observables.extend(["nph", "displ", "displ^2"])
# Run-time global variables
itern = 0 # iteration counter
verbose = verbose and mpi.is_master_node() # output is only produced by the master node
store_steps = store_steps and mpi.is_master_node() # output is only produced by the master node
symtype = ("QS" if B is None else "QSZ")
# Set up the Solver
S = Solver(model=model, symtype=symtype, mesh_max=mesh_max, mesh_min=mesh_min, mesh_ratio=mesh_ratio)
S.set_verbosity(verbose_nrg)
newG = lambda : S.G_w.copy() # Creates a BlockGf object of appropriate structure
nr_blocks = lambda bgf : len([bl for bl in bgf.indices]) # Returns the number of blocks in a BlockGf object
block_size = lambda bl : len(S.G_w[bl].indices[0]) # Matrix size of Green's functions in block 'bl'
identity = lambda bl : np.identity(block_size(bl)) # Returns the identity matrix in block 'bl'
# Solve Parameters
sp = { "T": T, "Lambda": 2.0, "Nz": 4, "Tmin": 1e-5, "keep": 10000, "keepenergy": 10.0 }
def _main_mpi(model_hdf5_file, input_file, output_file):
"""
Launch SumkDFT and compute chemical potential, local Green's function and density matrix
This function depends on MPI through DFTTools.
Do not call this from non-MPI module directly.
"""
import triqs.utility.mpi as mpi
# read HDF5 file on the master node
if mpi.is_master_node():
with HDFArchive(input_file, 'r') as h:
params = h['params']
keys = list(params.keys())
else:
params = {}
keys = []
assert isinstance(params, dict)
# broadcast parameters
keys = mpi.bcast(keys)
for key in keys:
if not mpi.is_master_node():
params[key] = None
params[key] = mpi.bcast(params[key])
beta = params['beta']
with_dc = params['with_dc']
results = {}
def add_potential(_sigma, _pot):
sigma_plus_pot = _sigma.copy()
for sp, sigma in sigma_plus_pot:
sigma += _pot[sp]
return sigma_plus_pot
def setup_sk(sk, iwn_or_w_or_none):
if iwn_or_w_or_none == 'iwn':
assert len(params['Sigma_iw_sh']) == len(params['potential'])
Sigma_iw_sh_plus_pot = [
add_potential(sigma, pot) for sigma, pot in zip(
params['Sigma_iw_sh'], params['potential'])
]
sk.set_Sigma(Sigma_iw_sh_plus_pot)
elif iwn_or_w_or_none == 'w':
# sk.set_Sigma([params['Sigma_w_sh'][ish] for ish in range(sk.n_inequiv_shells)])
Sigma_w_sh = [
params['Sigma_w_sh'][ish] for ish in range(sk.n_inequiv_shells)
]
Sigma_w_sh_plus_pot = [
add_potential(sigma, pot)
for sigma, pot in zip(Sigma_w_sh, params['potential'])
]
sk.set_Sigma(Sigma_w_sh_plus_pot)
elif iwn_or_w_or_none == "none":
pass
else:
raise RuntimeError("Invalid iwn_or_w")
if params['with_dc']:
sk.set_dc(params['dc_imp'], params['dc_energ'])
sk.set_mu(params['mu'])
if params['calc_mode'] == 'Gloc':
from triqs_dft_tools import SumkDFT
sk = SumkDFT(hdf_file=model_hdf5_file,
use_dft_blocks=False,
h_field=0.0)
setup_sk(sk, 'iwn')
if params['adjust_mu']:
# find the chemical potential for given density
sk.calc_mu(params['prec_mu'])
results['mu'] = float(sk.chemical_potential)
# Local Green's function and Density matrix
results['Gloc_iw_sh'] = sk.extract_G_loc(with_dc=with_dc)
dm = sk.density_matrix(beta=beta)
for ish in range(len(dm)):
for b in list(dm[ish].keys()):
dm[ish][b] = numpy.conj(dm[ish][b])
results['dm_sh'] = dm
elif params['calc_mode'] == 'dos':
# Compute dos
from .sumkdft_post import SumkDFTDCorePost
sk = SumkDFTDCorePost(hdf_file=model_hdf5_file,
use_dft_blocks=False,
h_field=0.0)
setup_sk(sk, 'w')
results['dos'], results['dosproj'], results['dosproj_orb'] = \
sk.dos_wannier_basis(broadening=params['broadening'],
mesh=params['mesh'],
with_Sigma=True, with_dc=with_dc, save_to_file=False)
elif params['calc_mode'] == 'spaghettis':
# A(k, omega)
from .sumkdft_post import SumkDFTDCorePost
sk = SumkDFTDCorePost(hdf_file=model_hdf5_file,
use_dft_blocks=False,
h_field=0.0,
bands_data=params['bands_data'])
setup_sk(sk, 'w')
results['akw'] = sk.spaghettis(broadening=params['broadening'],
plot_range=None,
ishell=None,
save_to_file=None)
elif params['calc_mode'] == 'momentum_distribution':
# n(k)
from .sumkdft_post import SumkDFTDCorePost
sk = SumkDFTDCorePost(hdf_file=model_hdf5_file,
use_dft_blocks=False,
h_field=0.0)
setup_sk(sk, 'iwn')
results['den'] = \
sk.calc_momentum_distribution(mu=params["mu"], beta=beta, with_Sigma=True, with_dc=True)
elif params['calc_mode'] == 'bse':
# chi0
from dft_tools.sumk_dft_chi import SumkDFTChi
# save div data (overwrite if data exist)
if mpi.is_master_node():
with HDFArchive(model_hdf5_file, 'a') as ar:
if 'dft_input_chi' in ar:
del ar['dft_input_chi']
ar.create_group('dft_input_chi')
ar['dft_input_chi']['div'] = numpy.array(params['div'])
# check if IBZ and FBZ data are saved separately
dft_data_fbz = 'dft_input'
if mpi.is_master_node():
with HDFArchive(model_hdf5_file, 'r') as ar:
if 'dft_input_fbz' in ar:
dft_data_fbz = 'dft_input_fbz'
dft_data_fbz = mpi.bcast(dft_data_fbz)
sk = SumkDFTChi(hdf_file=model_hdf5_file,
use_dft_blocks=False,
h_field=0.0,
dft_data_fbz=dft_data_fbz)
setup_sk(sk, 'iwn')
temp_file = None
if params['use_temp_file']:
temp_file = 'G_k_iw_temp.h5'
sk.save_X0q_for_bse(list_wb=params['list_wb'],
n_wf_cutoff=params['n_wf_G2'],
qpoints_saved=params['X0q_qpoints_saved'],
h5_file=params['bse_h5_out_file'],
temp_file=temp_file,
nonlocal_order_parameter=False)
else:
raise RuntimeError("Unknown calc_mode: " + str(params['calc_mode']))
if mpi.is_master_node():
with HDFArchive(output_file, 'w') as h:
for k, v in list(results.items()):
h[k] = v
def plot(filename):
if mpi.is_master_node():
with ar.HDFArchive(filename, 'r') as arch:
parms = arch["parms"]
t1 = parms['t1']
gimp = arch["G_iw"][ref_spin]
ref = arch["ref"]
sigma_k = HDFArchive("sigma_k.h5", 'r')['sigma_k'][ref_spin]
G_k = HDFArchive("G_k.h5", 'r')['G_k'][ref_spin]
inv = np.linalg.inv
# Calculate lattice self-energy
for ki, k in enumerate(sigma_k.mesh[1]):
selfenergylist = []
ref_list = []
simp_list = []
kx = k.value[0]
tk = -2 * t1 * (np.cos(kx))
def factor(ii):
return np.exp(1j * kx * ii)
for wn in sigma_k.mesh[0]:
wval = wn.value.imag
if wval < 0: continue
S = sigma_k[(wn, k)] + parms['chemical_potential']
invG0k = wn.value + parms['chemical_potential'] - tk
#S = invG0k-1./G_k[(wn,k)]
selfenergylist.append([
wval,
] + list(S.flatten()))
# Reference data, convert from 2x2 matrix to complex number with correct k
ref_G = np.sum(
factor(ii) * ref[(wn)][0, ii] for ii in range(2))
ref_S = invG0k - 1. / ref_G
ref_list.append([
wval,
] + list(ref_S.flatten()))
#ref_list.append( [wval,]+list(ref_G.flatten()) )
# calculate impurity self-energy as well, from runfile['G_iw']
g = gimp[(wn)]
# This was done using TODO check factors Delta
invg0 = wn.value + parms[
'chemical_potential'] - bath_prefactor**2 * 4 * t1**2 / (
wn.value + parms['chemical_potential_bare'])
Simp = invg0 - 1. / g
simp_list.append([
wval,
] + list(Simp.flatten()))
s = np.array(selfenergylist)
r = np.array(ref_list)
s2 = np.array(simp_list)
for column in range(1, 2):
assert np.max(np.abs(s[:5, column] - r[:5, column])) < 1e-4
def imtime_bubble_chi0_wk(g_wk, nw=1, save_memory=False):
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:
if not save_memory:
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
elif save_memory:
chi0_wr = chi0_wr_from_grt_PH(g_tr, nw=nw)
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 dmft_step(self, Delta_in):
self.itern += 1
if verbose():
print("\nIteration %i min_iter=%i max_iter=%i" %
(self.itern, self.dmft_param["min_iter"],
self.dmft_param["max_iter"]))
Delta_in_fixed = fix_hyb_function(Delta_in,
self.dmft_param["Delta_min"])
self.S.Delta_w << Delta_in_fixed
t0 = timeit.default_timer()
self.S.solve(**self.sp) # Solve the impurity model
t1 = timeit.default_timer()
dt = int(t1 - t0)
solver_time = '{:02}:{:02}:{:02}'.format(dt // 3600, dt % 3600 // 60,
dt % 60) # hh:mm:ss format
self.Gself = calc_G(
Delta_in_fixed, self.S.Sigma_w,
self.mu) # impurity GF ("self-energy-trick" improved)
Gloc_prev = self.Gloc.copy(
) # store copy of previous Gloc for checking convergence
self.Gloc, self.Delta = self_consistency(
self.S.Sigma_w, self.mu,
self.ht) # apply the DMFT self-consistency equation
self.occupancy = calc_occupancy(
self.Delta, self.S.Sigma_w, self.mu,
self.T) # occupancy calculated from the local lattice GF
diff_loc_imp = gf_diff(
self.Gself,
self.Gloc) # difference between impurity and local lattice GF
diff_prev = gf_diff(
self.Gloc, Gloc_prev
) # difference between two consecutively computed local latice GFs
diff_occupancy = abs(
self.occupancy - self.occupancy_goal
) # this difference is used as the measure of deviation
stats = OrderedDict([("itern", self.itern), ("time", solver_time),
("mu", self.mu), ("diff_loc_imp", diff_loc_imp),
("diff_prev", diff_prev),
("diff_occupancy", diff_occupancy),
("occupancy", self.occupancy)])
for i in self.observables:
stats[i] = self.S.expv[i]
header_string = fmt_str_header(
len(stats)).format(*[i for i in stats.keys()])
stats_string = fmt_str(len(stats)).format(*[i for i in stats.values()])
if mpi.is_master_node():
if self.itern == 1:
print(header_string, file=self.stats_file)
print(stats_string, file=self.stats_file)
if verbose():
print(header_string)
print(stats_string)
if self.dmft_param["store_steps"] and mpi.is_master_node():
os.mkdir(str(self.itern)) # one subdirectory per iteration
save_BlockGf(str(self.itern) + "/Delta", Delta_in_fixed)
save_BlockGf(str(self.itern) + "/Sigma",
self.S.Sigma_w) # self-energy
save_BlockGf(str(self.itern) + "/G",
self.Gloc) # local lattice Green's function
save_BlockA(str(self.itern) + "/A",
self.Gloc) # spectral function of local lattice GF
self.store_result(str(self.itern) + "/" + self.solution_filename)
if mpi.is_master_node():
self.store_result(self.checkpoint_filename
) # for checkpoint/restart functionality
# Check for convergence
if (diff_loc_imp < self.dmft_param["eps_loc_imp"]
and diff_prev < self.dmft_param["eps_prev"]
and diff_occupancy < self.dmft_param["eps_occupancy"]):
self.okn += 1
else:
self.okn = 0
# The only way to exit the DMFT loop is by generating exceptions.
if (self.okn >= self.dmft_param.get("conv_iter", 1)
and self.itern >= self.dmft_param["min_iter"]):
if mpi.is_master_node():
self.store_result(self.solution_filename
) # full converged results as an HDF5 file
try:
os.remove(self.checkpoint_filename
) # checkpoint file is no longer needed
except OSError:
pass
if self.converged_flag_file:
touch(self.converged_flag_file
) # signal convergence through a file
raise Converged("%s\n%s" % (header_string, stats_string))
if (self.itern == self.dmft_param["max_iter"]):
raise FailedToConverge("%s\n%s" % (header_string, stats_string))
if self.stop_flag_file and os.path.isfile(self.stop_flag_file):
raise ForcedStop()
if self.dmft_param["occup_method"] == "adjust":
self.Gloc, self.Delta, new_mu = self.adjust_mu(
self.Delta, self.S.Sigma_w,
self.mu) # here we update mu to get closer to target occupancy
self.set_mu(new_mu)
return self.Delta
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
S = Solver(**constr_params)
# --------- Initialize G0_iw ----------
S.G0_iw << G0_iw
# --------- Solve! ----------
solve_params = {
'h_int': h_int,
'n_warmup_cycles': 100,
'n_cycles': 1000,
'length_cycle': 100
}
S.solve(**solve_params)
# -------- Save in archive ---------
if mpi.is_master_node():
with HDFArchive("2orb_Discrete_Bath.out.h5", 'w') as results:
results["G_iw"] = S.G_iw
results["G_tau"] = S.G_tau
from triqs.utility.h5diff import h5diff
if args.libcxx:
h5diff("2orb_Discrete_Bath.libcxx.ref.h5",
"2orb_Discrete_Bath.out.h5",
precision=1.e-5)
elif args.gccver_ge11:
h5diff("2orb_Discrete_Bath.gccver_ge11.ref.h5",
"2orb_Discrete_Bath.out.h5",
precision=1.e-5)
else:
h5diff("2orb_Discrete_Bath.ref.h5",
def verbose():
return be_verbose and mpi.is_master_node()