def test_solver(chempot, u_int, gend):
parms = SOLVER_PARAMS
parms.update(U=u_int, MU=chempot, group='1band{}/'.format(u_int))
tau, w_n, g0t, Giw, v, intm = hf.setup_PM_sim(parms)
G0iw = 1 / (1j * w_n + parms['MU'] - .25 * Giw)
g0t = hf.gw_invfouriertrans(G0iw, tau, w_n, [1., -parms['MU'], 0.])
gtu, gtd = hf.imp_solver([g0t, g0t], v, intm, parms)
g = np.squeeze(0.5 * (gtu + gtd))
assert np.allclose(gend, g, atol=6e-3)
def test_solver(chempot, u_int, gend):
parms = {'BETA': 16., 'N_TAU': 2**11, 'N_MATSUBARA': 64,
't': 0.5,
'MU': chempot, 'U': u_int, 'dtau_mc': 0.5, 'n_tau_mc': 32,
'sweeps': 5000}
tau, w_n, g0t, Giw, v = hf.setup_PM_sim(parms)
G0iw = 1/(1j*w_n + parms['MU'] - .25*Giw)
G0t = hf.gw_invfouriertrans(G0iw, tau, w_n)
g0t = hf.interpol(G0t, parms['n_tau_mc'])
gtu, gtd = hf.imp_solver(g0t, g0t, v, parms['sweeps'])
g = -0.5 * (gtu+gtd)
assert np.allclose(gend, g, atol=6e-3)
def test_solver_atom(u_int):
parms = SOLVER_PARAMS
parms.update(U=u_int, group='atom{}/'.format(u_int))
v = hf.ising_v(parms['dtau_mc'], parms['U'], L=2 * parms['N_MATSUBARA'])
tau = np.linspace(0, parms['BETA'], 2 * parms['N_MATSUBARA'])
intm = hf.interaction_matrix(1) # one orbital
g0t = -.5 * np.ones(len(tau))
parms['work_dir'] = os.path.join(parms['ofile'], 'saves')
gtu, gtd = hf.imp_solver([g0t, g0t], v, intm, parms)
g = np.squeeze(-0.5 * (gtu + gtd)) # make positive for next log
result = np.polyfit(tau[:10], np.log(g[:10]), 1)
assert np.allclose(result, [-u_int / 2., np.log(.5)], atol=0.02)
def test_solver_dimer(chempot, u_int, gend):
parms = SOLVER_PARAMS
parms.update(U=u_int,
MU=chempot,
work_dir='dimer{}/'.format(u_int),
SITES=2)
tau, w_n, g0t, Giw, v, intm = hf.setup_PM_sim(parms)
G0iw = 1 / (1j * w_n + parms['MU'] - .25 * Giw)
G0t = hf.gw_invfouriertrans(G0iw, tau, w_n, [1., -parms['MU'], 0.])
gb0t = np.array([[G0t, np.zeros_like(G0t)], [np.zeros_like(G0t), G0t]])
gtu, gtd = hf.imp_solver([gb0t] * 2, v, intm, parms)
g = np.squeeze(0.5 * (gtu + gtd))
assert np.allclose(gend, g[0, 0], atol=6e-3)
assert np.allclose(np.zeros_like(g0t), g[0, 1], atol=6e-3)
assert np.allclose(np.zeros_like(g0t), g[1, 0], atol=6e-3)
assert np.allclose(gend, g[1, 1], atol=6e-3)
def test_solver(chempot, u_int, gend):
parms = {
'BETA': 16.,
'N_TAU': 2**11,
'N_MATSUBARA': 64,
't': 0.5,
'MU': chempot,
'U': u_int,
'dtau_mc': 0.5,
'n_tau_mc': 32,
'sweeps': 5000
}
tau, w_n, g0t, Giw, v = hf.setup_PM_sim(parms)
G0iw = 1 / (1j * w_n + parms['MU'] - .25 * Giw)
G0t = hf.gw_invfouriertrans(G0iw, tau, w_n)
g0t = hf.interpol(G0t, parms['n_tau_mc'])
gtu, gtd = hf.imp_solver(g0t, g0t, v, parms['sweeps'])
g = -0.5 * (gtu + gtd)
assert np.allclose(gend, g, atol=6e-3)
def dmft_loop_pm(gw=None, **kwargs):
"""Implementation of the solver"""
parameters = {
'n_tau_mc': 40,
'BETA': 16,
'N_TAU': 2**11,
'N_MATSUBARA': 64,
'U': 2,
't': 0.5,
'MU': 0,
'loops': 8,
'sweeps': 20000,
}
tau, w_n, __, Giw, v_aux = hf.setup_PM_sim(parameters)
simulation = {'parameters': parameters}
if gw is not None:
Giw = gw
for iter_count in range(parameters['loops']):
G0iw = 1/(1j*w_n + parameters['MU'] - parameters['t']**2 * Giw)
G0t = gw_invfouriertrans(G0iw, tau, w_n)
g0t = hf.interpol(G0t, parameters['n_tau_mc'])
gtu, gtd = hf.imp_solver(g0t, g0t, v_aux, parameters['sweeps'])
gt = -0.5 * (gtu+gtd)
Gt = hf.interpol(gt, parameters['N_TAU'])
Giw = gt_fouriertrans(Gt, tau, w_n)
simulation['it{:0>2}'.format(iter_count)] = {
'G0iw': G0iw,
'Giw': Giw,
'gtau': gt,
}
return simulation
def dmft_loop_pm(gw=None, **kwargs):
"""Implementation of the solver"""
parameters = {
'n_tau_mc': 40,
'BETA': 16,
'N_TAU': 2**11,
'N_MATSUBARA': 64,
'U': 2,
't': 0.5,
'MU': 0,
'loops': 8,
'sweeps': 20000,
}
tau, w_n, __, Giw, v_aux = hf.setup_PM_sim(parameters)
simulation = {'parameters': parameters}
if gw is not None:
Giw = gw
for iter_count in range(parameters['loops']):
G0iw = 1 / (1j * w_n + parameters['MU'] - parameters['t']**2 * Giw)
G0t = gw_invfouriertrans(G0iw, tau, w_n)
g0t = hf.interpol(G0t, parameters['n_tau_mc'])
gtu, gtd = hf.imp_solver(g0t, g0t, v_aux, parameters['sweeps'])
gt = -0.5 * (gtu + gtd)
Gt = hf.interpol(gt, parameters['N_TAU'])
Giw = gt_fouriertrans(Gt, tau, w_n)
simulation['it{:0>2}'.format(iter_count)] = {
'G0iw': G0iw,
'Giw': Giw,
'gtau': gt,
}
return simulation
def dmft_loop_pm(simulation, U, g_iw_start=None):
"""Implementation of the solver"""
setup = {
't': 0.5,
'BANDS': 1,
'SITES': 2,
}
setup.update(simulation)
setup['dtau_mc'] = setup['BETA'] / 2. / setup['N_MATSUBARA']
current_u = 'U' + str(U)
setup['U'] = U
setup['simt'] = 'PM' # simulation type ParaMagnetic
if setup['AFM']:
setup['simt'] = 'AFM' # simulation type AntiFerroMagnetic
tau, w_n = gf.tau_wn_setup(setup)
intm = hf.interaction_matrix(setup['BANDS'])
setup['n_tau_mc'] = len(tau)
mu, tp = setup['MU'], setup['tp']
giw_d, giw_o = dimer.gf_met(w_n, mu, tp, 0.5, 0.)
gmix = np.array([[1j * w_n + mu, -tp * np.ones_like(w_n)],
[-tp * np.ones_like(w_n), 1j * w_n + mu]])
giw = np.array([[giw_d, giw_o], [giw_o, giw_d]])
g0tau0 = -0.5 * np.eye(2).reshape(2, 2, 1)
gtu = gf.gw_invfouriertrans(giw, tau, w_n, pd.gf_tail(g0tau0, 0., mu, tp))
gtd = np.copy(gtu)
if g_iw_start is not None:
giw_up = g_iw_start[0]
giw_dw = g_iw_start[1]
save_dir = os.path.join(setup['ofile'].format(**setup), current_u)
try: # try reloading data from disk
with open(save_dir + '/setup', 'r') as conf:
last_loop = json.load(conf)['last_loop']
gtu = np.load(
os.path.join(save_dir, 'it{:03}'.format(last_loop),
'gtau_up.npy')).reshape(2, 2, -1)
gtd = np.load(
os.path.join(save_dir, 'it{:03}'.format(last_loop),
'gtau_dw.npy')).reshape(2, 2, -1)
last_loop += 1
except (IOError, KeyError, ValueError): # if no data clean start
last_loop = 0
V_field = hf.ising_v(setup['dtau_mc'],
U,
L=setup['SITES'] * setup['n_tau_mc'],
polar=setup['spin_polarization'])
for iter_count in range(last_loop, last_loop + setup['Niter']):
work_dir = os.path.join(save_dir, 'it{:03}'.format(iter_count))
setup['work_dir'] = work_dir
if comm.rank == 0:
print('On loop', iter_count, 'beta', setup['BETA'], 'U', U, 'tp',
tp)
# paramagnetic cleaning
gtu = 0.5 * (gtu + gtd)
gtd = gtu
giw_up = gf.gt_fouriertrans(gtu, tau, w_n, pd.gf_tail(gtu, U, mu, tp))
giw_dw = gf.gt_fouriertrans(gtd, tau, w_n, pd.gf_tail(gtd, U, mu, tp))
# Bethe lattice bath
g0iw_up = dimer.mat_2_inv(gmix - 0.25 * giw_up)
g0iw_dw = dimer.mat_2_inv(gmix - 0.25 * giw_dw)
g0tau_up = gf.gw_invfouriertrans(g0iw_up, tau, w_n,
pd.gf_tail(g0tau0, 0., mu, tp))
g0tau_dw = gf.gw_invfouriertrans(g0iw_dw, tau, w_n,
pd.gf_tail(g0tau0, 0., mu, tp))
# Impurity solver
gtu, gtd = hf.imp_solver([g0tau_dw, g0tau_up], V_field, intm, setup)
# Save output
if comm.rank == 0:
np.save(work_dir + '/gtau_up', gtu.reshape(4, -1))
np.save(work_dir + '/gtau_dw', gtd.reshape(4, -1))
with open(save_dir + '/setup', 'w') as conf:
setup['last_loop'] = iter_count
json.dump(setup, conf, indent=2)
sys.stdout.flush()
def dmft_loop_pm(simulation):
"""Implementation of the solver"""
setup = {
't': 0.5,
'BANDS': 1,
'SITES': 2,
}
if simulation['new_seed']:
if comm.rank == 0:
hf.set_new_seed(simulation, ['gtau_d', 'gtau_o'])
simulation['U'] = simulation['new_seed'][1]
return
setup.update(simulation)
setup['dtau_mc'] = setup['BETA'] / 2. / setup['N_MATSUBARA']
current_u = 'U' + str(setup['U'])
tau, w_n = gf.tau_wn_setup(setup)
intm = hf.interaction_matrix(setup['BANDS'])
setup['n_tau_mc'] = len(tau)
mu, tp, U = setup['MU'], setup['tp'], setup['U']
giw_d_up, giw_o_up = dimer.gf_met(w_n, 1e-3, tp, 0.5, 0.)
giw_d_dw, giw_o_dw = dimer.gf_met(w_n, -1e-3, tp, 0.5, 0.)
gmix = np.array([[1j * w_n, -tp * np.ones_like(w_n)],
[-tp * np.ones_like(w_n), 1j * w_n]])
g0tail = [
np.eye(2).reshape(2, 2, 1),
tp * np.array([[0, 1], [1, 0]]).reshape(2, 2, 1),
np.array([[tp**2, 0], [0, tp**2]]).reshape(2, 2, 1)
]
gtail = [
np.eye(2).reshape(2, 2, 1),
tp * np.array([[0, 1], [1, 0]]).reshape(2, 2, 1),
np.array([[tp**2 + U**2 / 4, 0], [0,
tp**2 + U**2 / 4]]).reshape(2, 2, 1)
]
giw_up = np.array([[giw_d_up, giw_o_up], [giw_o_dw, giw_d_dw]])
giw_dw = np.array([[giw_d_dw, giw_o_dw], [giw_o_up, giw_d_up]])
try: # try reloading data from disk
with h5.File(setup['ofile'].format(**setup), 'r') as last_run:
last_loop = len(last_run[current_u].keys())
last_it = 'it{:03}'.format(last_loop - 1)
giw_d, giw_o = pd.get_giw(last_run[current_u], last_it, tau, w_n)
except (IOError, KeyError): # if no data clean start
last_loop = 0
V_field = hf.ising_v(setup['dtau_mc'],
setup['U'],
L=setup['SITES'] * setup['n_tau_mc'],
polar=setup['spin_polarization'])
for loop_count in range(last_loop, last_loop + setup['Niter']):
# For saving in the h5 file
dest_group = current_u + '/it{:03}/'.format(loop_count)
setup['group'] = dest_group
if comm.rank == 0:
print('On loop', loop_count, 'beta', setup['BETA'], 'U', U, 'tp',
tp)
# Bethe lattice bath
g0iw_up = mat_2_inv(gmix - 0.25 * giw_up)
g0iw_dw = mat_2_inv(gmix - 0.25 * giw_dw)
g0tau_up = gf.gw_invfouriertrans(g0iw_up, tau, w_n, g0tail)
g0tau_dw = gf.gw_invfouriertrans(g0iw_dw, tau, w_n, g0tail)
# Impurity solver
gtu, gtd = hf.imp_solver([g0tau_up, g0tau_dw], V_field, intm, setup)
giw_up = gf.gt_fouriertrans(-gtu, tau, w_n, gtail)
giw_dw = gf.gt_fouriertrans(-gtd, tau, w_n, gtail)
# Save output
if comm.rank == 0:
with h5.File(setup['ofile'].format(**setup), 'a') as store:
store[dest_group + 'gtau_u'] = gtu
store[dest_group + 'gtau_d'] = gtd
h5.add_attributes(store[dest_group], setup)
sys.stdout.flush()
def dmft_loop_pm(simulation, U, g_iw_start=None):
"""Implementation of the solver"""
setup = {'t': .5,
'SITES': 1,
}
current_u = 'U'+str(U)
setup.update(simulation)
setup['U'] = U
setup['simt'] = 'PM' # simulation type ParaMagnetic
tau, w_n, _, giw, v_aux, intm = hf.setup_PM_sim(setup)
if setup['AFM']:
giw = giw + np.array([[-1], [1]])*1e-3*giw.imag
setup['simt'] = 'AFM' # simulation type Anti-Ferro-Magnetic
if g_iw_start is not None:
giw = g_iw_start
gtau = gf.gw_invfouriertrans(giw, tau, w_n, [1., 0., .25])
save_dir = os.path.join(setup['ofile'].format(**setup), current_u)
try:
with open(save_dir + '/setup', 'r') as conf:
last_loop = json.load(conf)['last_loop']
gtau = np.load(os.path.join(save_dir,
'it{:03}'.format(last_loop),
'gtau.npy'))
last_loop += 1
except (IOError, OSError):
last_loop = 0
for iter_count in range(last_loop, last_loop + setup['Niter']):
# For saving in the h5 file
work_dir = os.path.join(save_dir, 'it{:03}'.format(iter_count))
setup['work_dir'] = work_dir
if COMM.rank == 0:
print('On loop', iter_count, 'beta', setup['BETA'], 'U', setup['U'])
giw = gf.gt_fouriertrans(gtau, tau, w_n,
pss.gf_tail(gtau, U, setup['MU']))
if setup['AFM']:
g0iw = 1/(1j*w_n + setup['MU'] - setup['t']**2 * giw[[1, 0]])
g0tau = gf.gw_invfouriertrans(g0iw, tau, w_n, [1., 0., .25])
gtu, gtd = hf.imp_solver([g0tau[0], g0tau[1]], v_aux, intm, setup)
gtau = np.squeeze([gtu, gtd])
else:
# enforce Half-fill, particle-hole symmetry
giw.real = 0.
g0iw = 1/(1j*w_n + setup['MU'] - setup['t']**2 * giw)
g0tau = gf.gw_invfouriertrans(g0iw, tau, w_n, [1., 0., .25])
gtu, gtd = hf.imp_solver([g0tau]*2, v_aux, intm, setup)
gtau = np.squeeze(0.5 * (gtu+gtd))
if COMM.rank == 0:
np.save(work_dir + '/gtau', gtau)
with open(save_dir + '/setup', 'w') as conf:
setup['last_loop'] = iter_count
json.dump(setup, conf, indent=2)
sys.stdout.flush()
return giw