def ipt_u_tp(u_int, tp, beta, seed='ins'):
tau, w_n = gf.tau_wn_setup(dict(BETA=beta, N_MATSUBARA=2**8))
tau, w_n = gf.tau_wn_setup(
dict(BETA=beta, N_MATSUBARA=max(2**ceil(log(8 * beta) / log(2)), 256)))
giw_d, giw_o = dimer.gf_met(w_n, 0., 0., 0.5, 0.)
if seed == 'ins':
giw_d, giw_o = 1 / (1j * w_n + 4j / w_n), np.zeros_like(w_n) + 0j
giw_d, giw_o, loops = dimer.ipt_dmft_loop(
beta, u_int, tp, giw_d, giw_o, tau, w_n, 1e-7)
g0iw_d, g0iw_o = dimer.self_consistency(
1j * w_n, 1j * giw_d.imag, giw_o.real, 0., tp, 0.25)
siw_d, siw_o = ipt.dimer_sigma(u_int, tp, g0iw_d, g0iw_o, tau, w_n)
return giw_d, giw_o, siw_d, siw_o, g0iw_d, g0iw_o, w_n
def energies(beta, filestr='SB_PM_B{}.h5'):
"""returns the potential, and kinetic energy
Parameters
----------
beta : float, inverse temperature
filestr : string, results file name, beta is replaced in format
Returns
-------
tuple of 3 ndarrays
Contains, potential energy, Kinetic energy, values of U
"""
tau, w_n = gf.tau_wn_setup(dict(BETA=beta, N_MATSUBARA=beta))
giw_free = gf.greenF(w_n)
e_mean = ipt.e_mean(beta)
ekin = []
epot = []
with h5.File(filestr.format(beta), 'r') as results:
for u_str in results:
last_iter = results[u_str].keys()[-1]
_, giw = get_giw(results[u_str], last_iter, tau, w_n)
siw = get_sigmaiw(results[u_str], last_iter, tau, w_n)
u_int = float(u_str[1:])
epot.append(ipt.epot(giw, siw, u_int, beta, w_n))
ekin.append(ipt.ekin(giw, siw, beta, w_n, e_mean, giw_free))
ur = np.array([float(u_str[1:]) for u_str in results])
return np.array(epot), np.array(ekin), ur
def show_conv(beta, u_int, filestr='SB_{simt}_B{beta}', n_freq=5, xlim=2, skip=5, simt='PM'):
"""Plot the evolution of the Green's function in DMFT iterations"""
freq_arr = []
sim_dir = os.path.join(filestr.format(
beta=beta, simt=simt), 'U' + str(u_int))
iterations = sorted(
[it for it in os.listdir(sim_dir) if 'it' in it])[skip:]
with open(sim_dir + '/setup', 'r') as read:
setup = json.load(read)
tau, w_n = gf.tau_wn_setup(setup)
_, axes = plt.subplots(1, 2, figsize=(13, 8), sharey=True)
for step in iterations:
giw, caste = get_giw(sim_dir, [step], tau, w_n, setup)
if len(giw.shape) > 1:
axes[0].plot(w_n, giw[0].real, 'gs:', w_n, giw[0].imag, 'bo:')
freq_arr.append(
np.array([giw[0].real[:n_freq], giw[0].imag[:n_freq]]))
else:
axes[0].plot(w_n, giw.imag)
freq_arr.append(giw.imag[:n_freq])
freq_arr = np.asarray(freq_arr).T
for num, freqs in enumerate(freq_arr):
axes[1].plot(freqs.T, 'o-.', label=str(num))
graf = r'$G(i\omega_n)$'
label_convergence(beta, u_int, axes, graf, n_freq, xlim)
return axes
def get_giw(sim_dir, iteration_slice, tau=None, w_n=None, setup=None):
r"""Recovers with Fourier Transform G_iw from H5 file
Parameters
----------
h5parent : hdf5 group to go
iteration_slice : list of iteration names to average over
tau : 1D real array time slices of HF data
w_n : 1D real array matsubara frequencies
Returns
-------
tuple : :math:`G(\tau)`, :math:`G(i\omega_n)`
"""
recovered_sim_info = False
if None in (tau, w_n, setup):
with open(sim_dir + '/setup', 'r') as read:
setup = json.load(read)
tau, w_n = gf.tau_wn_setup(setup)
recovered_sim_info = True
gtau = averager(sim_dir, 'gtau.npy', iteration_slice)
giw = gf.gt_fouriertrans(gtau, tau, w_n,
gf_tail(gtau, setup['U'], setup['MU']))
if recovered_sim_info:
return giw, gtau, tau, w_n, setup
else:
return giw, gtau
def estimate_zero_w_sigma_T_vs_U(tp, u_range, temp, phase):
sd_zew, so_zew = [], []
u_range = u_range if phase == 'met' else u_range[::-1]
save_file = 'dimer_ipt_{}_Z_tp{:.2}.npy'.format(phase, tp)
if os.path.exists(save_file):
return np.load(save_file)
for T in temp:
beta = 1 / T
tau, w_n = gf.tau_wn_setup(
dict(BETA=beta, N_MATSUBARA=max(2**ceil(log(6 * beta) / log(2)), 256)))
filestr = 'disk/phase_Dimer_ipt_{}_tp{:.2}/B{:.5}/giw.npy'.format(
phase, tp, beta)
gfs = np.load(filestr)
for i, u_int in enumerate(u_range):
giw_d, giw_o = 1j * gfs[i][0], gfs[i][1]
g0iw_d, g0iw_o = dimer.self_consistency(
1j * w_n, giw_d, giw_o, 0., tp, 0.25)
siw_d, siw_o = ipt.dimer_sigma(u_int, tp, g0iw_d, g0iw_o, tau, w_n)
sd_zew.append(np.polyfit(w_n[:2], siw_d[:2].imag, 1))
so_zew.append(np.polyfit(w_n[:2], siw_o[:2].real, 1))
sd_zew = np.array(sd_zew).reshape(len(temp), len(u_range), -1)
so_zew = np.array(so_zew).reshape(len(temp), len(u_range), -1)
np.save(save_file, (sd_zew, so_zew))
return sd_zew, so_zew
def loop_tp_u(tprange, u_range, beta, filestr, seed='mott gap'):
save_dir = filestr.format(beta)
if np.allclose(tprange, tprange[0]) and 'tp' not in save_dir:
save_dir = os.path.join(save_dir, 'tp' + str(tprange[0]))
elif np.allclose(u_range, u_range[0]):
save_dir = os.path.join(save_dir, 'U' + str(u_range[0]))
if not os.path.exists(save_dir):
os.makedirs(save_dir)
setup = {
'beta': beta,
'tprange': tprange.tolist(),
'u_range': u_range.tolist()
}
with open(save_dir + '/setup', 'w') as conf:
json.dump(setup, conf, indent=2)
###############################################################################
tau, w_n = gf.tau_wn_setup(
dict(BETA=beta, N_MATSUBARA=max(2**ceil(log(6 * beta) / log(2)), 256)))
giw_d, giw_o = dimer.gf_met(w_n, 0., tprange[0], 0.5, 0.)
if seed == 'mott gap':
giw_d, giw_o = 1 / (1j * w_n - 4j / w_n), np.zeros_like(w_n) + 0j
giw_s = []
for tp, u_int in zip(tprange, u_range):
giw_d, giw_o, loops = dimer.ipt_dmft_loop(beta, u_int, tp, giw_d,
giw_o, tau, w_n,
1 / 5 / beta)
giw_s.append((giw_d.imag, giw_o.real))
np.save(save_dir + '/giw', np.array(giw_s))
def plot_zero_w(function_array, iter_range, tp, betarange, ax, color):
"""Plot the zero frequency extrapolation of a function
Parameters
----------
function_array: real ndarray
contains the function (G, Sigma) to linearly fit over 2 first frequencies
iter_range: list floats
values of changing variable U or tp
berarange: real ndarray 1D, values of beta
entry: 0, 1 corresponds to diagonal or off-diagonal entry of function
label_head: string for label
ax, dx: matplotlib axis to plot in
"""
sig_11_0 = []
rtp = []
for j, u in enumerate(iter_range):
sig_11_0.append([])
rtp.append([])
for i, beta in list(enumerate(betarange)):
tau, w_n = gf.tau_wn_setup(dict(BETA=beta, N_MATSUBARA=2))
sig_11_0[j].append(np.polyfit(
w_n, function_array[j][i][0][:2], 1)[1])
rtp[j].append(np.polyfit(w_n, function_array[j][i][1][:2], 1)[1])
ax[0].plot(1 / BETARANGE, -np.array(sig_11_0[j]), color, label=str(u))
ax[1].plot(1 / BETARANGE, tp + np.array(rtp[j]), color, label=str(u))
ax[0].set_ylabel(r'$-\Im m \Sigma_{11}(w=0)$')
ax[1].set_ylabel(r'$t_\perp + \Re e\Sigma_{12}(w=0)$')
ax[1].set_xlabel('$T/D$')
ax[1].set_xlim([min(temp), max(temp)])
return np.array(sig_11_0)
def test_ipt_dimer_pm_g(u_int, result, beta=50.):
tau, w_n = tau_wn_setup(dict(BETA=beta, N_MATSUBARA=256))
giw_d, giw_o = dimer.gf_met(w_n, 0., 0, 0.5, 0.)
giw_d = dimer.ipt_dmft_loop(beta, u_int, 0, giw_d, giw_o, tau, w_n,
1e-5)[0][:64]
assert np.allclose(result, giw_d, atol=3e-3)
def loop_u_tp(u_range, tp_range, beta, seed='mott gap'):
"""Solves IPT dimer and return Im Sigma_AA, Re Simga_AB
returns list len(betarange) x 2 Sigma arrays
"""
tau, w_n = gf.tau_wn_setup(
dict(BETA=beta, N_MATSUBARA=max(2**ceil(log(4 * beta) / log(2)), 256)))
giw_d, giw_o = dimer.gf_met(w_n, 0., 0., 0.5, 0.)
if seed == 'I':
giw_d, giw_o = 1 / (1j * w_n - 4j / w_n), np.zeros_like(w_n) + 0j
sigma_iw = []
iterations = []
for tp, u_int in zip(tp_range, u_range):
giw_d, giw_o, loops = dimer.ipt_dmft_loop(beta, u_int, tp, giw_d,
giw_o, tau, w_n, 1e-3)
iterations.append(loops)
g0iw_d, g0iw_o = dimer.self_consistency(1j * w_n, 1j * giw_d.imag,
giw_o.real, 0., tp, 0.25)
siw_d, siw_o = ipt.dimer_sigma(u_int, tp, g0iw_d, g0iw_o, tau, w_n)
sigma_iw.append((siw_d.imag, siw_o.real))
print(np.array(iterations))
return sigma_iw
def test_selfconsistency(tp):
"""Check that the Bethe lattice self-consistency is working"""
_, w_n = tau_wn_setup(dict(BETA=100., N_MATSUBARA=400))
giwd, giwo = dimer.gf_met(w_n, 0., tp, 0.5, 0.)
g0iwd, g0iwo = dimer.self_consistency(1j * w_n, giwd, giwo, 0., tp, 0.25)
assert np.allclose(giwd, g0iwd)
assert np.allclose(giwo, g0iwo)
def loop_u_tp(u_range, tprange, beta, seed='mott gap'):
tau, w_n = gf.tau_wn_setup(dict(BETA=beta, N_MATSUBARA=max(5 * beta, 256)))
giw_d, giw_o = dimer.gf_met(w_n, 0., 0., 0.5, 0.)
if seed == 'mott gap':
giw_d, giw_o = 1 / (1j * w_n + 4j / w_n), np.zeros_like(w_n) + 0j
giw_s = []
sigma_iw = []
ekin, epot = [], []
iterations = []
for u_int, tp in zip(u_range, tprange):
giw_d, giw_o, loops = dimer.ipt_dmft_loop(beta, u_int, tp, giw_d,
giw_o, tau, w_n)
giw_s.append((giw_d, giw_o))
iterations.append(loops)
g0iw_d, g0iw_o = dimer.self_consistency(1j * w_n, 1j * giw_d.imag,
giw_o.real, 0., tp, 0.25)
siw_d, siw_o = ipt.dimer_sigma(u_int, tp, g0iw_d, g0iw_o, tau, w_n)
sigma_iw.append((siw_d.copy(), siw_o.copy()))
ekin.append(dimer.ekin(giw_d, giw_o, w_n, tp, beta))
epot.append(
dimer.epot(giw_d, w_n, beta, u_int**2 / 4 + tp**2, ekin[-1], u_int)
/ 4) # last division because I want per spin epot
print(np.array(iterations))
return np.array(giw_s), np.array(sigma_iw), np.array(ekin), np.array(
epot), w_n
def free_energy_change(beta, u_int, mix_grid):
tau, w_n = tau_wn_setup(dict(BETA=beta, N_MATSUBARA=2**11))
ig_iwn, is_iwn = dmft_loop(u_int,
0.5,
-1.j / (w_n - 1 / w_n),
w_n,
tau,
conv=1e-10)
mg_iwn, ms_iwn = dmft_loop(u_int, 0.5, greenF(w_n), w_n, tau, conv=1e-10)
solution_diff = mg_iwn - ig_iwn
integrand = []
for l in mix_grid:
g_in = mix(mg_iwn, ig_iwn, l)
g_grad = one_loop(g_in, 0.5, U, w_n, tau) - g_in
integrand.append(np.dot(g_grad, solution_diff).real / beta)
return np.array([0] + [
trapz(integrand[:i], mix_grid[:i])
for i in range(2,
len(mix_grid) + 1)
])
def hysteresis(beta, u_range):
log_g_sig = []
tau, w_n = tau_wn_setup(dict(BETA=beta, N_MATSUBARA=beta))
g_iwn = greenF(w_n)
for u_int in u_range:
g_iwn, sigma = dmft_loop(u_int, 0.5, g_iwn, w_n, tau)
log_g_sig.append((g_iwn, sigma))
return log_g_sig
def hysteresis(beta, D_range):
log_g_sig = []
tau, w_n = tau_wn_setup(dict(BETA=beta, N_MATSUBARA=2**11))
g_iwn = greenF(w_n, D=1)
for D in D_range:
g_iwn, sigma = dmft_loop(1, D / 2, g_iwn, w_n, tau)
log_g_sig.append((g_iwn, sigma))
return log_g_sig
def extract_double_occupation(beta, u_range):
docc = []
tau, w_n = gf.tau_wn_setup(dict(BETA=beta, N_MATSUBARA=beta))
g_iwn = gf.greenF(w_n)
for u_int in u_range:
g_iwn, sigma = ipt.dmft_loop(u_int, 0.5, g_iwn, w_n, tau, conv=1e-4)
docc.append(ipt.epot(g_iwn, sigma, u_int, beta, w_n) * 2 / u_int)
return np.array(docc)
def setup_PM_sim(parms):
tau, w_n = tau_wn_setup(parms)
gw = greenF(w_n, mu=parms['MU'], D=2 * parms['t'])
gt = gw_invfouriertrans(gw, tau, w_n)
gt = interpol(gt, parms['n_tau_mc'])
parms['dtau_mc'] = parms['BETA'] / parms['n_tau_mc']
v = ising_v(parms['dtau_mc'], parms['U'], L=parms['n_tau_mc'])
return tau, w_n, gt, gw, v
def test_ipt_pm_g(u_int, result, beta=50., n_tau=2**11, n_matsubara=64):
parms = {'BETA': beta, 'N_TAU': n_tau, 'N_MATSUBARA': n_matsubara,
't': 0.5, 'MU': 0, 'U': u_int,
}
tau, w_n = tau_wn_setup(parms)
g_iwn0 = greenF(w_n, D=2*parms['t'])
g_iwn_log, sigma_iwn = ipt_imag.dmft_loop(100, parms['U'], parms['t'], g_iwn0, w_n, tau)
assert np.allclose(result, g_iwn_log[-1][32:], atol=1e-3 )
def setup_PM_sim(parms):
tau, w_n = tau_wn_setup(parms)
gw = greenF(w_n, mu=parms['MU'], D=2*parms['t'])
gt = gw_invfouriertrans(gw, tau, w_n)
gt = interpol(gt, parms['n_tau_mc'])
parms['dtau_mc'] = parms['BETA']/parms['n_tau_mc']
v = ising_v(parms['dtau_mc'], parms['U'], L=parms['n_tau_mc'])
return tau, w_n, gt, gw, v
def test_fourier_trasforms(chempot, beta=50., n_matsubara=128):
"""Test the tail improved fourier transforms"""
parms = {'BETA': beta, 'N_MATSUBARA': n_matsubara}
tau, w_n = gf.tau_wn_setup(parms)
giw = gf.greenF(w_n, mu=chempot)
for gwr in [giw, np.array([giw, giw])]:
g_tau = gf.gw_invfouriertrans(gwr, tau, w_n, [1., -chempot, 0.25])
g_iomega = gf.gt_fouriertrans(g_tau, tau, w_n, [1., -chempot, 0.25])
assert np.allclose(gwr, g_iomega)
def test_fourier_trasforms(chempot, beta=50., n_tau=2**11, n_matsubara=64):
"""Test the tail improved fourier transforms"""
parms = {'BETA': beta, 'N_TAU': n_tau, 'N_MATSUBARA': n_matsubara}
tau, w_n = tau_wn_setup(parms)
gw = greenF(w_n, mu=chempot)
for gwr in [gw, np.array([gw, gw])]:
g_tau = gw_invfouriertrans(gwr, tau, w_n)
g_iomega = gt_fouriertrans(g_tau, tau, w_n)
assert np.allclose(gwr, g_iomega)
def test_fourier_trasforms(chempot, beta=50., n_tau=2**11, n_matsubara=64):
"""Test the tail improved fourier transforms"""
parms = {'BETA': beta, 'N_TAU': n_tau, 'N_MATSUBARA': n_matsubara}
tau, w_n = tau_wn_setup(parms)
gw = greenF(w_n, mu=chempot)
for gwr in [gw, np.array([gw, gw])]:
g_tau = gw_invfouriertrans(gwr, tau, w_n)
g_iomega = gt_fouriertrans(g_tau, tau, w_n)
assert np.allclose(gwr, g_iomega)
def collect_bined_saves():
binede_dat = glob('gtau_bin_*')
G = np.array([np.load(dfile) for dfile in binede_dat])
gtau = G.mean(1)
tau, w_n = gf.tau_wn_setup(dict(BETA=32., N_MATSUBARA=32))
fw = gf.matsubara_freq(32., 64, -63)
giw = gf.gt_fouriertrans(gtau, tau, w_n, [1., 0., .25 + 2.5**2 / 4])
sgiw = np.concatenate((giw.conj().T[::-1], giw.T))
np.savez('bined', w_n=fw, giw=sgiw)
def test_GF():
"""Test the Matrix product and Matrix inversion of a 2x2 Matrix
which for the case of the dimer has a symmetric structure in which
only requires the first row"""
_, w_n = tau_wn_setup(dict(BETA=100., N_MATSUBARA=400))
giwd, giwo = dimer.gf_met(w_n, 0., 0.25, 0.5, 0.)
inv_giwd, inv_giwo = dimer.mat_inv(giwd, giwo)
one, zero = dimer.mat_mul(inv_giwd, inv_giwo, giwd, giwo)
assert np.allclose(one, 1.)
assert np.allclose(zero, 0.)
def setup_PM_sim(parms):
"""Setup the default state for a Paramagnetic simulation"""
tau, w_n = tau_wn_setup(parms)
giw = greenF(w_n, mu=parms['MU'], D=2 * parms['t'])
gtau = gw_invfouriertrans(giw, tau, w_n)
parms['dtau_mc'] = tau[1]
intm = interaction_matrix(parms.get('BANDS', 1))
v = ising_v(parms['dtau_mc'], parms['U'],
len(tau) * parms['SITES'], intm.shape[1],
parms['spin_polarization'])
return tau, w_n, gtau, giw, v, intm
def ipt_u_tp(u_int, tp, beta, seed="ins"):
tau, w_n = gf.tau_wn_setup(dict(BETA=beta, N_MATSUBARA=1024))
giw_d, giw_o = dimer.gf_met(w_n, 0., 0., 0.5, 0.)
if seed == "ins":
giw_d, giw_o = 1 / (1j * w_n + 4j / w_n), np.zeros_like(w_n) + 0j
giw_d, giw_o, loops = dimer.ipt_dmft_loop(
beta, u_int, tp, giw_d, giw_o, tau, w_n, 1e-12)
g0iw_d, g0iw_o = dimer.self_consistency(
1j * w_n, 1j * giw_d.imag, giw_o.real, 0., tp, 0.25)
siw_d, siw_o = ipt.dimer_sigma(u_int, tp, g0iw_d, g0iw_o, tau, w_n)
return giw_d, giw_o, siw_d, siw_o, g0iw_d, g0iw_o, w_n
def test_ipt_pm_g(u_int, result, beta=50., n_matsubara=64):
"""Test the solution of the single band impurity problem"""
parms = {
'BETA': beta,
'N_MATSUBARA': n_matsubara,
't': 0.5,
'MU': 0,
'U': u_int,
}
tau, w_n = tau_wn_setup(parms)
g_iwn0 = greenF(w_n, D=2 * parms['t'])
g_iwn, _ = ipt_imag.dmft_loop(parms['U'], parms['t'], g_iwn0, w_n, tau)
assert np.allclose(result, g_iwn, atol=3e-3)
def loop_urange(urange, tp, beta):
ekin, epot = [], []
tau, w_n = gf.tau_wn_setup(dict(BETA=beta, N_MATSUBARA=2**10))
giw_d, giw_o = dimer.gf_met(w_n, 0., 0., 0.5, 0.)
for u_int in urange:
giw_d, giw_o, _ = dimer.ipt_dmft_loop(beta, u_int, tp, giw_d, giw_o,
tau, w_n, 1e-4)
ekin.append(dimer.ekin(giw_d, giw_o, w_n, tp, beta))
epot.append(
dimer.epot(giw_d, w_n, beta, u_int**2 / 4 + tp**2 + 0.25, ekin[-1],
u_int))
return np.array(ekin), np.array(epot)
def test_ipt_pm_g(u_int, result, beta=50., n_tau=2**11, n_matsubara=64):
parms = {
'BETA': beta,
'N_TAU': n_tau,
'N_MATSUBARA': n_matsubara,
't': 0.5,
'MU': 0,
'U': u_int,
}
tau, w_n = tau_wn_setup(parms)
g_iwn0 = greenF(w_n, D=2 * parms['t'])
g_iwn_log, sigma_iwn = ipt_imag.dmft_loop(100, parms['U'], parms['t'],
g_iwn0, w_n, tau)
assert np.allclose(result, g_iwn_log[-1][32:], atol=1e-3)
def dos_plot(BETA, tp, filestr, ax=None):
"""Plots double occupation"""
if ax is None:
_, ax = plt.subplots()
with h5.File(filestr.format(tp=tp, BETA=BETA), 'r') as results:
fl_dos = []
tau, w_n = gf.tau_wn_setup(dict(BETA=BETA, N_MATSUBARA=BETA))
for u_str in results:
lastit = results[u_str].keys()[-1]
giwd, _ = get_giw(results[u_str], lastit, tau, w_n)
fl_dos.append(-1. / np.pi * gf.fit_gf(w_n[:3], giwd.imag)(0.))
u_range = np.array([float(u_str[1:]) for u_str in results.keys()])
ax.scatter(u_range, fl_dos, s=120, marker='>', vmin=0, vmax=2. / np.pi)
ax.set_title('Hysteresis loop of the \n density of states')
ax.set_ylabel(r'$A(\omega=0)$')
ax.set_xlabel('U/D')
def loop_u_tp(u_range, tprange, beta, seed='mott gap'):
tau, w_n = gf.tau_wn_setup(dict(BETA=beta, N_MATSUBARA=max(5 * beta, 256)))
giw_d, giw_o = dimer.gf_met(w_n, 0., 0., 0.5, 0.)
if seed == 'mott gap':
giw_d, giw_o = 1 / (1j * w_n + 4j / w_n), np.zeros_like(w_n) + 0j
sigma_iw = []
for u_int, tp in zip(u_range, tprange):
giw_d, giw_o, loops = dimer.ipt_dmft_loop(
beta, u_int, tp, giw_d, giw_o, tau, w_n)
g0iw_d, g0iw_o = dimer.self_consistency(
1j * w_n, 1j * giw_d.imag, giw_o.real, 0., tp, 0.25)
siw_d, siw_o = ipt.dimer_sigma(u_int, tp, g0iw_d, g0iw_o, tau, w_n)
sigma_iw.append((siw_d.copy(), siw_o.copy()))
print(seed, ' U', u_int, ' tp: ', tp, ' loops: ', loops)
return np.array(sigma_iw), w_n
def loop_u_tp(u_range, tprange, beta, seed='mott gap'):
tau, w_n = gf.tau_wn_setup(dict(BETA=beta, N_MATSUBARA=256))
giw_d, giw_o = dimer.gf_met(w_n, 0., 0., 0.5, 0.)
if seed == 'ins':
giw_d, giw_o = 1 / (1j * w_n + 4j / w_n), np.zeros_like(w_n) + 0j
sols = [dmft_solve(giw_d, giw_o, u_int, tp, beta, tau, w_n)
for u_int, tp in zip(u_range, tprange)]
giw_s = np.array([g[0] for g in sols])
sigma_iw = np.array([g[1] for g in sols])
ekin = np.array([g[2] for g in sols])
epot = np.array([g[3] for g in sols])
iterations = np.array([g[4] for g in sols])
print(iterations)
return giw_s, sigma_iw, ekin, epot, w_n
def get_giw(filestr, tau=None, w_n=None, setup=None):
"""Recovers with Fourier Transform G_iw and G_tau from npy file
Parameters
----------
filestr : string
file with array data G(tau)
setup : dictionary about simulation parameters
tau : real float array
Imaginary time points
w_n : real float array
fermionic matsubara frequencies. Only use the positive ones
Returns
-------
tuple complex ndarray (giw, gtau)
Interacting Greens function in matsubara frequencies
and original Imaginary time. Entries are list ordered and
not in matrix shape
See also
--------
get_sigmaiw
"""
recovered_sim_info = False
if None in (tau, w_n, setup):
sim_dir = os.path.dirname(os.path.dirname(os.path.abspath(filestr)))
with open(sim_dir + '/setup', 'r') as read:
setup = json.load(read)
tau, w_n = gf.tau_wn_setup(setup)
recovered_sim_info = True
gtau = np.load(filestr)
mu, tp, u_int = setup['MU'], setup['tp'], setup['U']
giw = gf.gt_fouriertrans(gtau.reshape(2, 2, -1), tau, w_n,
gf_tail(gtau.reshape(2, 2, -1), u_int, mu, tp))
if recovered_sim_info:
return giw.reshape(4, -1), gtau, tau, w_n, setup
else:
return giw.reshape(4, -1), gtau
def plot_zero_w(function_array, iter_range, beta, entry, label_head, ax, dx):
"""Plot the zero frequency extrapolation of a function
Parameters
----------
function_array: real ndarray
contains the function (G, Sigma) to linearly fit over 2 first frequencies
iter_range: list floats
values of changing variable U or tp
berarange: real ndarray 1D, values of beta
entry: 0, 1 corresponds to diagonal or off-diagonal entry of function
label_head: string for label
ax, dx: matplotlib axis to plot in
"""
tau, w_n = gf.tau_wn_setup(dict(BETA=beta, N_MATSUBARA=20))
dat = []
for j, u in enumerate(iter_range):
dat.append(np.polyfit(w_n[:2], function_array[j][entry][:2], 1))
ax.plot(iter_range, -np.array(dat)[:, 1], label=label_head)
dx.plot(iter_range, -np.array(dat)[:, 0], label=label_head)
from dmft.common import greenF, tau_wn_setup
from dmft.twosite import matsubara_Z
import numpy as np
import matplotlib.pylab as plt
U = np.linspace(0, 2.7, 36)
U = np.concatenate((U, U[-2:11:-1]))
parms = {'MU': 0, 't': 0.5, 'N_TAU': 2**10, 'N_MATSUBARA': 2**7}
lop_g=[]
for beta in [16, 25, 50]:
u_zet = []
parms['BETA'] = beta
tau, w_n = tau_wn_setup(parms)
g_iwn0 = greenF(w_n, D=2*parms['t'])
for u_int in U:
mix = 0.4 if u_int > 1.5 else 1
g_iwn_log, sigma = ipt_imag.dmft_loop(100, u_int, parms['t'], g_iwn0, w_n, tau, mix)
g_iwn0 = g_iwn_log[-1]
lop_g.append(g_iwn_log)
u_zet.append(matsubara_Z(sigma.imag, beta))
plt.plot(U, u_zet, label='$\\beta={}$'.format(beta))
plt.title('Hysteresis loop of the quasiparticle weigth')
plt.legend()
plt.ylabel('Z')
plt.xlabel('U/D')
