def _frequency_shifts_at_bands(self, i, bi, freqs, interaction, weight):
sum_d = 0
for (j, k) in list(np.ndindex(interaction.shape[1:])):
if (freqs[1, j] > self._cutoff_frequency and
freqs[2, k] > self._cutoff_frequency):
d = 0.0
n2 = occupation(freqs[1, j], self._temperature)
n3 = occupation(freqs[2, k], self._temperature)
f1 = freqs[0, bi] + freqs[1, j] + freqs[2, k]
f2 = freqs[0, bi] - freqs[1, j] - freqs[2, k]
f3 = freqs[0, bi] - freqs[1, j] + freqs[2, k]
f4 = freqs[0, bi] + freqs[1, j] - freqs[2, k]
# if abs(f1) > self._epsilon:
# d -= (n2 + n3 + 1) / f1
# if abs(f2) > self._epsilon:
# d += (n2 + n3 + 1) / f2
# if abs(f3) > self._epsilon:
# d -= (n2 - n3) / f3
# if abs(f4) > self._epsilon:
# d += (n2 - n3) / f4
d -= (n2 + n3 + 1) * f1 / (f1 ** 2 + self._epsilon ** 2)
d += (n2 + n3 + 1) * f2 / (f2 ** 2 + self._epsilon ** 2)
d -= (n2 - n3) * f3 / (f3 ** 2 + self._epsilon ** 2)
d += (n2 - n3) * f4 / (f4 ** 2 + self._epsilon ** 2)
sum_d += d * interaction[i, j, k] * weight
return sum_d
def _ise_at_bands(self, i, bi, freqs, interaction, weight):
sum_g = 0
for (j, k) in list(np.ndindex(interaction.shape[1:])):
if (freqs[1][j] > self._cutoff_frequency and
freqs[2][k] > self._cutoff_frequency):
n2 = occupation(freqs[1][j], self._temperature)
n3 = occupation(freqs[2][k], self._temperature)
g1 = gaussian(freqs[0, bi] - freqs[1, j] - freqs[2, k],
self._sigma)
g2 = gaussian(freqs[0, bi] + freqs[1, j] - freqs[2, k],
self._sigma)
g3 = gaussian(freqs[0, bi] - freqs[1, j] + freqs[2, k],
self._sigma)
sum_g += ((n2 + n3 + 1) * g1 +
(n2 - n3) * (g2 - g3)) * interaction[i, j, k] * weight
return sum_g
def _run_c_with_g(self, is_band_freq=False):
self.set_phonons(self._triplets_at_q.ravel())
if is_band_freq == True:
self._frequency_points = self._frequencies[self._grid_point]
else:
if self._sigma is None:
f_max = np.max(self._frequencies) * 2
else:
f_max = np.max(self._frequencies) * 2 + self._sigma * 4
f_max *= 1.005
f_min = 0
self._set_frequency_points(f_min, f_max)
num_freq_points = len(self._frequency_points)
num_mesh = np.prod(self._mesh)
if self._temperatures is None:
jdos = np.zeros((num_freq_points, 2), dtype='double')
else:
num_temps = len(self._temperatures)
jdos = np.zeros((num_temps, num_freq_points, 2), dtype='double')
occ_phonons = []
for t in self._temperatures:
freqs = self._frequencies[self._triplets_at_q[:, 1:]]
occ_phonons.append(np.where(freqs > self._cutoff_frequency,
occupation(freqs, t), 0))
for i, freq_point in enumerate(self._frequency_points):
g = get_triplets_integration_weights(
self,
np.array([freq_point], dtype='double'),
self._sigma,
neighboring_phonons=(i == 0),
is_triplet_symmetry=False)
if self._temperatures is None:
jdos[i, 1] = np.sum(
np.tensordot(g[0, :, 0], self._weights_at_q, axes=(0, 0)))
# gx = g[2] - g[0]
gx = g[1] + g[2]
jdos[i, 0] = - np.sum(
np.tensordot(gx[:, 0], self._weights_at_q, axes=(0, 0)))# the negative sign is for a clearer plot
else:
# g1 = g[1]
g1 = g[2] - g[1]
for j, n in enumerate(occ_phonons): # loop over temperature
for k, l in list(np.ndindex(g.shape[3:])): # double loop over other two phonon branches
jdos[j, i, 1] += np.dot(
(n[:, 0, k] + n[:, 1, l] + 1) *
g[0, :, 0, k, l], self._weights_at_q)
jdos[j, i, 0] += - np.dot((n[:, 0, k] - n[:, 1, l]) *
g1[:, 0, k, l],
self._weights_at_q) # the negative sign is for a clearer plot
self._joint_dos = jdos / num_mesh
def _ise_thm_with_frequency_points(self):
for i, (tp, w, interaction) in enumerate(zip(self._triplets_at_q,
self._weights_at_q,
self._fc3_normal_squared)):
for j, k in list(np.ndindex(interaction.shape[1:])):
f1 = self._frequencies[tp[1]][j]
f2 = self._frequencies[tp[2]][k]
if (f1 > self._cutoff_frequency and
f2 > self._cutoff_frequency):
n2 = occupation(f1, self._temperature)
n3 = occupation(f2, self._temperature)
g1 = self._g[0, i, :, j, k]
g2_g3 = self._g[1, i, :, j, k] # g2 - g3
for l in range(len(interaction)):
self._imag_self_energy[:, l] += (
(n2 + n3 + 1) * g1 +
(n2 - n3) * (g2_g3)) * interaction[l, j, k] * w
self._imag_self_energy *= self._unit_conversion
def _ise_with_frequency_points(self, freqs, interaction, weight):
for j, k in list(np.ndindex(interaction.shape[1:])):
if (freqs[0][j] > self._cutoff_frequency and
freqs[1][k] > self._cutoff_frequency):
n2 = occupation(freqs[0][j], self._temperature)
n3 = occupation(freqs[1][k], self._temperature)
g1 = gaussian(self._frequency_points
- freqs[0][j] - freqs[1][k], self._sigma)
g2 = gaussian(self._frequency_points
+ freqs[0][j] - freqs[1][k], self._sigma)
g3 = gaussian(self._frequency_points
- freqs[0][j] + freqs[1][k], self._sigma)
else:
continue
for i in range(len(interaction)):
self._imag_self_energy[:, i] += (
(n2 + n3 + 1) * g1 +
(n2 - n3) * (g2 - g3)) * interaction[i, j, k] * weight
def _ise_thm_with_frequency_points(self):
for i, (tp, w, interaction) in enumerate(zip(self._triplets_at_q,
self._weights_at_q,
self._pp_strength)):
for j, k in list(np.ndindex(interaction.shape[1:])):
f1 = self._frequencies[tp[1]][j]
f2 = self._frequencies[tp[2]][k]
if (f1 > self._cutoff_frequency and
f2 > self._cutoff_frequency):
n2 = occupation(f1, self._temperature)
n3 = occupation(f2, self._temperature)
g1 = self._g[0, i, :, j, k]
g2_g3 = self._g[1, i, :, j, k] # g2 - g3
for l in range(len(interaction)):
self._imag_self_energy[:, l] += (
(n2 + n3 + 1) * g1 +
(n2 - n3) * (g2_g3)) * interaction[l, j, k] * w
self._imag_self_energy *= self._unit_conversion
def _ise_with_frequency_points(self, freqs, interaction, weight):
for j, k in list(np.ndindex(interaction.shape[1:])):
if (freqs[0][j] > self._cutoff_frequency and
freqs[1][k] > self._cutoff_frequency):
n2 = occupation(freqs[0][j], self._temperature)
n3 = occupation(freqs[1][k], self._temperature)
g1 = gaussian(self._frequency_points
- freqs[0][j] - freqs[1][k], self._sigma)
g2 = gaussian(self._frequency_points
+ freqs[0][j] - freqs[1][k], self._sigma)
g3 = gaussian(self._frequency_points
- freqs[0][j] + freqs[1][k], self._sigma)
else:
continue
for i in range(len(interaction)):
self._imag_self_energy[:, i] += (
(n2 + n3 + 1) * g1 +
(n2 - n3) * (g2 - g3)) * interaction[i, j, k] * weight
def _run_c_with_g(self):
self.set_phonon(self._triplets_at_q.ravel())
if self._sigma is None:
f_max = np.max(self._frequencies) * 2
else:
f_max = np.max(self._frequencies) * 2 + self._sigma * 4
f_max *= 1.005
f_min = 0
self._set_uniform_frequency_points(f_min, f_max)
num_freq_points = len(self._frequency_points)
num_mesh = np.prod(self._mesh)
if self._temperatures is None:
jdos = np.zeros((num_freq_points, 2), dtype='double')
else:
num_temps = len(self._temperatures)
jdos = np.zeros((num_temps, num_freq_points, 2), dtype='double')
occ_phonons = []
for t in self._temperatures:
freqs = self._frequencies[self._triplets_at_q[:, 1:]]
occ_phonons.append(
np.where(freqs > self._cutoff_frequency,
occupation(freqs, t), 0))
for i, freq_point in enumerate(self._frequency_points):
g = get_triplets_integration_weights(self,
np.array([freq_point],
dtype='double'),
self._sigma,
is_collision_matrix=True,
neighboring_phonons=(i == 0))
if self._temperatures is None:
jdos[i, 1] = np.sum(
np.tensordot(g[0, :, 0], self._weights_at_q, axes=(0, 0)))
gx = g[2] - g[0]
jdos[i, 0] = np.sum(
np.tensordot(gx[:, 0], self._weights_at_q, axes=(0, 0)))
else:
for j, n in enumerate(occ_phonons):
for k, l in list(np.ndindex(g.shape[3:])):
jdos[j, i, 1] += np.dot(
(n[:, 0, k] + n[:, 1, l] + 1) * g[0, :, 0, k, l],
self._weights_at_q)
jdos[j, i, 0] += np.dot(
(n[:, 0, k] - n[:, 1, l]) * g[1, :, 0, k, l],
self._weights_at_q)
self._joint_dos = jdos / num_mesh
def _run_c_with_g(self):
self.set_phonon(self._triplets_at_q.ravel())
if self._sigma is None:
f_max = np.max(self._frequencies) * 2
else:
f_max = np.max(self._frequencies) * 2 + self._sigma * 4
f_max *= 1.005
f_min = 0
self._set_frequency_points(f_min, f_max)
num_freq_points = len(self._frequency_points)
num_mesh = np.prod(self._mesh)
if self._temperatures is None:
jdos = np.zeros((num_freq_points, 2), dtype='double')
else:
num_temps = len(self._temperatures)
jdos = np.zeros((num_temps, num_freq_points, 2), dtype='double')
occ_phonons = []
for t in self._temperatures:
freqs = self._frequencies[self._triplets_at_q[:, 1:]]
occ_phonons.append(np.where(freqs > self._cutoff_frequency,
occupation(freqs, t), 0))
for i, freq_point in enumerate(self._frequency_points):
g = get_triplets_integration_weights(
self,
np.array([freq_point], dtype='double'),
self._sigma,
is_collision_matrix=True,
neighboring_phonons=(i == 0))
if self._temperatures is None:
jdos[i, 0] = np.sum(
np.tensordot(g[0, :, 0], self._weights_at_q, axes=(0, 0)))
gx = g[2] - g[0]
jdos[i, 1] = np.sum(
np.tensordot(gx[:, 0], self._weights_at_q, axes=(0, 0)))
else:
for j, n in enumerate(occ_phonons):
for k, l in list(np.ndindex(g.shape[3:])):
jdos[j, i, 0] += np.dot(
(n[:, 0, k] + n[:, 1, l] + 1) *
g[0, :, 0, k, l], self._weights_at_q)
jdos[j, i, 1] += np.dot((n[:, 0, k] - n[:, 1, l]) *
g[1, :, 0, k, l],
self._weights_at_q)
self._joint_dos = jdos / num_mesh
def _ise_thm_with_band_indices(self):
freqs = self._frequencies[self._triplets_at_q[:, [1, 2]]]
freqs = np.where(freqs > self._cutoff_frequency, freqs, 1)
n = occupation(freqs, self._temperature)
for i, (tp, w, interaction) in enumerate(zip(self._triplets_at_q,
self._weights_at_q,
self._fc3_normal_squared)):
for j, k in list(np.ndindex(interaction.shape[1:])):
f1 = self._frequencies[tp[1]][j]
f2 = self._frequencies[tp[2]][k]
if (f1 > self._cutoff_frequency and
f2 > self._cutoff_frequency):
n2 = n[i, 0, j]
n3 = n[i, 1, k]
g1 = self._g[0, i, :, j, k]
g2_g3 = self._g[1, i, :, j, k] # g2 - g3
self._imag_self_energy[:] += (
(n2 + n3 + 1) * g1 +
(n2 - n3) * (g2_g3)) * interaction[:, j, k] * w
self._imag_self_energy *= self._unit_conversion
def _ise_thm_with_band_indices(self):
freqs = self._frequencies[self._triplets_at_q[:, [1, 2]]]
freqs = np.where(freqs > self._cutoff_frequency, freqs, 1)
n = occupation(freqs, self._temperature)
for i, (tp, w, interaction) in enumerate(
zip(self._triplets_at_q, self._weights_at_q,
self._pp_strength)):
for j, k in list(np.ndindex(interaction.shape[1:])):
f1 = self._frequencies[tp[1]][j]
f2 = self._frequencies[tp[2]][k]
if (f1 > self._cutoff_frequency
and f2 > self._cutoff_frequency):
n2 = n[i, 0, j]
n3 = n[i, 1, k]
g1 = self._g[0, i, :, j, k]
g2_g3 = self._g[1, i, :, j, k] # g2 - g3
self._imag_self_energy[:] += (
(n2 + n3 + 1) * g1 + (n2 - n3) *
(g2_g3)) * interaction[:, j, k] * w
self._imag_self_energy *= self._unit_conversion