def get_C4z_symmetry_map(config):
assert config.n_sublattices == 1
geometry = 'square'
mapping = np.zeros((config.total_dof // 2, config.total_dof // 2)) + 0.0j # trivial mapping
rotation_matrix = np.array([[np.cos(2 * np.pi / 4.), np.sin(2 * np.pi / 4.)], \
[-np.sin(2 * np.pi / 4.), np.cos(2 * np.pi / 4.)]])
if config.n_orbitals == 2:
rotation_matrix_orbital = rotation_matrix
else:
rotation_matrix_orbital = np.eye(1)
for preindex in range(config.total_dof // 2):
orbit_preimage, sublattice_preimage, x_preimage, y_preimage = \
models.from_linearized_index(preindex, config.Ls, config.n_orbitals, config.n_sublattices)
orbit_preimage_vector = np.zeros(config.n_orbitals); orbit_preimage_vector[orbit_preimage] = 1.
r_preimage = models.lattice_to_physical([x_preimage, y_preimage, sublattice_preimage], geometry)
orbit_image_vector = np.einsum('ij,j->i', rotation_matrix_orbital, orbit_preimage_vector)
r_image = np.einsum('ij,j->i', rotation_matrix, r_preimage)
x_image, y_image, sublattice_image = models.physical_to_lattice(r_image, geometry)
x_image = int(np.rint(x_image)); y_image = int(np.rint(y_image))
x_image = (x_image % config.Ls); y_image = (y_image % config.Ls)
for orbit_image in range(config.n_orbitals):
coefficient = orbit_image_vector[orbit_image]
index = models.to_linearized_index(x_image, y_image, sublattice_image, orbit_image, \
config.Ls, config.n_orbitals, config.n_sublattices)
mapping[preindex, index] += coefficient
assert np.sum(np.abs(mapping.dot(mapping).dot(mapping).dot(mapping) - np.eye(mapping.shape[0]))) < 1e-5 # C_4z^4 = I
return mapping + 0.0j
def get_C2y_symmetry_map_chiral_jastrow(config):
mapping = np.zeros((config.total_dof // 2, config.total_dof // 2))
for preindex in range(config.total_dof // 2):
orbit_preimage, sublattice_preimage, x_preimage, y_preimage = \
models.from_linearized_index(preindex, config.Ls, config.n_orbitals, config.n_sublattices)
orbit_image = 1 - orbit_preimage
r_preimage = np.array(
models.lattice_to_physical(
[x_preimage, y_preimage, sublattice_preimage],
'hexagonal'))
r_preimage -= np.array([1. / np.sqrt(3) / 2, 0.0])
r_image = np.array([-r_preimage[0], r_preimage[1]]) + np.array(
[1. / np.sqrt(3) / 2, 0.0])
x_image, y_image, sublattice_image = models.physical_to_lattice(
r_image, 'hexagonal')
x_image = int(np.rint(x_image))
y_image = int(np.rint(y_image))
x_image = (x_image % config.Ls)
y_image = (y_image % config.Ls)
index = models.to_linearized_index(x_image, y_image, sublattice_image, orbit_image, \
config.Ls, config.n_orbitals, config.n_sublattices)
mapping[preindex, index] += 1.
assert np.sum(np.abs(mapping.dot(mapping) -
np.eye(mapping.shape[0]))) < 1e-12 # C_2y^2 = I
return mapping
def get_TRS_symmetry_map_chiral_jastrow(config):
assert config.n_sublattices == 2
geometry = 'hexagonal'
mapping = np.zeros(
(config.total_dof // 2, config.total_dof // 2)) # trivial mapping
for preindex in range(config.total_dof // 2):
orbit_preimage, sublattice_preimage, x_preimage, y_preimage = \
models.from_linearized_index(preindex, config.Ls, config.n_orbitals, config.n_sublattices)
r_preimage = models.lattice_to_physical(
[x_preimage, y_preimage, sublattice_preimage], geometry)
r_image = r_preimage
x_image, y_image, sublattice_image = models.physical_to_lattice(
r_image, geometry)
x_image = int(np.rint(x_image))
y_image = int(np.rint(y_image))
x_image = (x_image % config.Ls)
y_image = (y_image % config.Ls)
index = models.to_linearized_index(x_image, y_image, sublattice_image, 1 - orbit_preimage, \
config.Ls, config.n_orbitals, config.n_sublattices)
mapping[preindex, index] = 1.
assert np.sum(np.abs(mapping.dot(mapping) -
np.eye(mapping.shape[0]))) < 1e-12 # T^2 = I
return mapping
def get_C3z_symmetry_map_chiral_jastrow(config):
assert config.n_sublattices == 2
geometry = 'hexagonal'
mapping = np.zeros(
(config.total_dof // 2, config.total_dof // 2)) # trivial mapping
rotation_matrix = np.array([[np.cos(2 * np.pi / 3.), np.sin(2 * np.pi / 3.)], \
[-np.sin(2 * np.pi / 3.), np.cos(2 * np.pi / 3.)]])
for preindex in range(config.total_dof // 2):
orbit_preimage, sublattice_preimage, x_preimage, y_preimage = \
models.from_linearized_index(preindex, config.Ls, config.n_orbitals, config.n_sublattices)
r_preimage = models.lattice_to_physical(
[x_preimage, y_preimage, sublattice_preimage], geometry)
r_image = np.einsum('ij,j->i', rotation_matrix, r_preimage)
x_image, y_image, sublattice_image = models.physical_to_lattice(
r_image, geometry)
x_image = int(np.rint(x_image))
y_image = int(np.rint(y_image))
x_image = (x_image % config.Ls)
y_image = (y_image % config.Ls)
index = models.to_linearized_index(x_image, y_image, sublattice_image, orbit_preimage, \
config.Ls, config.n_orbitals, config.n_sublattices)
mapping[preindex, index] = 1.
assert np.sum(
np.abs(
mapping.dot(mapping).dot(mapping) -
np.eye(mapping.shape[0]))) < 1e-12 # C_3z^3 = I
return mapping
def K_FT(k, K, config, R, spin_dof=1):
L = config.Ls
n_internal = config.n_sublattices * config.n_orbitals * spin_dof
result = np.zeros((n_internal, n_internal)) * 1.0j
#result = np.zeros((n_internal // 2, n_internal // 2)) * 1.0j
x1, y1 = 0, 0 # rely on translational invariance
for sublattice_orbit_spin1 in range(n_internal):
### parse mega-index into components ###
spin1 = sublattice_orbit_spin1 % spin_dof
sublattice1 = (sublattice_orbit_spin1 //
spin_dof) % config.n_sublattices
orbit1 = ((sublattice_orbit_spin1 // spin_dof) //
config.n_sublattices) % config.n_orbitals
first = models.to_linearized_index(x1, y1, sublattice1, orbit1, L, \
config.n_orbitals, config.n_sublattices) + spin1 * (K.shape[0] // spin_dof)
for second in range(K.shape[0]):
spin2 = second // (K.shape[0] // spin_dof)
orbit2, sublattice2, x2, y2 = models.from_linearized_index(second % (K.shape[0] // spin_dof), L, \
config.n_orbitals, config.n_sublattices)
element = K[first, second]
r2_real = np.einsum('j,jk->k', np.array([x2 - x1, y2 - y1]), R)
ft_factor = np.exp(1.0j * np.einsum('i,i', r2_real, k))
result[(orbit1 + config.n_orbitals * sublattice1) + spin1 * result.shape[0] // 2, \
(orbit2 + config.n_orbitals * sublattice2) + spin2 * result.shape[0] // 2] += ft_factor * element
#if spin1 == 0 and spin2 == 0:
# result[orbit1 + config.n_orbitals * sublattice1, \
# orbit2 + config.n_orbitals * sublattice2] += ft_factor * element
return result
def expand_tensor_product(config, sigma_l1l2, sigma_o1o2, delta_ij, spin_ij = np.eye(1)):
'''
returns the matrix of the dimention L x L (L -- total number of sites including orbit),
sigma_ll \\otimes sigma_oo \\otimes delta_ii
'''
spin_factor = spin_ij.shape[0]
if spin_factor > 1:
Delta = np.zeros((config.total_dof, config.total_dof)) * 1.0j
else:
Delta = np.zeros((config.total_dof // 2, config.total_dof // 2)) * 1.0j
for first in range(Delta.shape[0]):
for second in range(Delta.shape[1]):
spin1 = first // (config.total_dof // 2)
spin2 = second // (config.total_dof // 2)
orbit1, sublattice1, x1, y1 = models.from_linearized_index(deepcopy(first % (config.total_dof // 2)), \
config.Ls, config.n_orbitals, config.n_sublattices)
orbit2, sublattice2, x2, y2 = models.from_linearized_index(deepcopy(second % (config.total_dof // 2)), \
config.Ls, config.n_orbitals, config.n_sublattices)
space1 = (x1 * config.Ls + y1) * config.n_sublattices + sublattice1
space2 = (x2 * config.Ls + y2) * config.n_sublattices + sublattice2
if config.n_sublattices == 2:
if sublattice2 - sublattice1 == 1: # AB pairings (only in the hexagonal case)
delta_s1s2 = delta_ij[0]
elif sublattice2 - sublattice1 == -1: # BA pairings (only in the hexagonal case)
delta_s1s2 = delta_ij[1]
elif sublattice1 == 0 and len(delta_ij) == 2:
delta_s1s2 = delta_ij[0] # AA pairing (only hex case, not on-site)
elif sublattice1 == 1 and len(delta_ij) == 2:
delta_s1s2 = delta_ij[1] # BB pairing (only hex case, not on-site)
else:
delta_s1s2 = delta_ij
else:
delta_s1s2 = delta_ij # only square case
# otherwise (subl2 = subl1 means this is a square lattice or hex on-site, just use the delta_ij matrix)
if sigma_l1l2[sublattice1, sublattice2] != 0.0:
Delta[first, second] = sigma_l1l2[sublattice1, sublattice2] * \
sigma_o1o2[orbit1, orbit2] * \
delta_s1s2[space1, space2] * \
spin_ij[spin1, spin2]
return Delta + 0.0j
def _get_ik_marking(Ls, n_orbitals, n_sublattices, total_dof):
A = np.zeros((total_dof // 2, total_dof // 2), dtype=np.int64)
for i in range(total_dof // 2):
oi, si, xi, yi = models.from_linearized_index(i, Ls, n_orbitals,
n_sublattices)
for j in range(total_dof // 2):
oj, sj, xj, yj = models.from_linearized_index(
j, Ls, n_orbitals, n_sublattices)
dx = (xi - xj) % Ls
dy = (yi - yj) % Ls
index_spatial = dy * Ls + dx
index_orbital = n_sublattices * n_sublattices * (
oi * n_sublattices + si) + (oj * n_sublattices + sj)
A[i,
j] = index_spatial * n_orbitals**2 * n_sublattices**2 + index_orbital
return A
def get_Ty_symmetry_map(config, chiral = False):
mapping = np.zeros((config.total_dof // 2, config.total_dof // 2)) + 0.0j # trivial mapping
for preindex in range(config.total_dof // 2):
orbit_preimage, sublattice_preimage, x_preimage, y_preimage = \
models.from_linearized_index(preindex, config.Ls, config.n_orbitals, config.n_sublattices)
index = models.to_linearized_index(x_preimage, (y_preimage + 1) % config.Ls, sublattice_preimage, orbit_preimage, \
config.Ls, config.n_orbitals, config.n_sublattices)
mapping[preindex, index] += 1.
trivial = np.eye(config.total_dof // 2)
for i in range(config.Ls):
trivial = trivial.dot(mapping)
assert np.allclose(trivial, np.eye(config.total_dof // 2))
return mapping + 0.0j
def get_C2y_symmetry_map(config, chiral = False):
if config.n_sublattices == 2:
geometry = 'hexagonal'
else:
geometry = 'square'
mapping = np.zeros((config.total_dof // 2, config.total_dof // 2)) + 0.0j # trivial mapping
for preindex in range(config.total_dof // 2):
orbit_preimage, sublattice_preimage, x_preimage, y_preimage = \
models.from_linearized_index(preindex, config.Ls, config.n_orbitals, config.n_sublattices)
if config.n_orbitals == 2:
if not chiral:
orbit_image = orbit_preimage
coefficient = -1.0 if orbit_image == 0 else 1.0
else:
orbit_image = 1 - orbit_preimage
coefficient = -1.0
else:
orbit_image = orbit_preimage
coefficient = 1.0
r_preimage = np.array(models.lattice_to_physical([x_preimage, y_preimage, sublattice_preimage], geometry))
if geometry == 'hexagonal':
r_preimage -= np.array([1. / np.sqrt(3) / 2, 0.0])
r_image = np.array([-r_preimage[0], r_preimage[1]]) + np.array([1. / np.sqrt(3) / 2, 0.0])
else:
r_image = np.array([-r_preimage[0], r_preimage[1]])
x_image, y_image, sublattice_image = models.physical_to_lattice(r_image, geometry)
x_image = int(np.rint(x_image)); y_image = int(np.rint(y_image))
x_image = (x_image % config.Ls); y_image = (y_image % config.Ls)
index = models.to_linearized_index(x_image, y_image, sublattice_image, orbit_image, \
config.Ls, config.n_orbitals, config.n_sublattices)
mapping[preindex, index] += coefficient
assert np.sum(np.abs(mapping.dot(mapping) - np.eye(mapping.shape[0]))) < 1e-5 # C_2y^2 = I
return mapping + 0.0j
def get_E_J_Hund_long(edges_J, wf_state, total_fugacity, twist, Ls, n_orbitals,
n_sublattices):
L = len(wf_state[3]) // 2
E_loc = 0.0 + 0.0j
for i in range(edges_J.shape[0] // 2):
for j in range(edges_J.shape[1] // 2):
if edges_J[i * 2, j * 2] == 0:
continue
for orb in range(2):
itotal = i * 2 + orb
jtotal = j * 2 + orb
orbiti, _, xi, yi = from_linearized_index(
itotal, Ls, n_orbitals, n_sublattices)
orbitj, _, xj, yj = from_linearized_index(
jtotal, Ls, n_orbitals, n_sublattices)
factor_x_up_up = 1.0
factor_x_up_down = 1.0
factor_x_down_up = 1.0
factor_x_down_down = 1.0
factor_y_up_up = 1.0
factor_y_up_down = 1.0
factor_y_down_up = 1.0
factor_y_down_down = 1.0
if np.abs(xi - xj) > Ls // 2:
factor_x_up_up = np.exp(-1.0j * twist[0] *
(-1. + 2 * orb) * (+1.0) +
1.0j * twist[0] * (-1. + 2 * orb) *
(+1.0))
factor_x_up_down = np.exp(-1.0j * twist[0] *
(-1. + 2 * orb) * (-1.0) +
1.0j * twist[0] *
(-1. + 2 * orb) * (+1.0))
factor_x_down_up = np.exp(-1.0j * twist[0] *
(-1. + 2 * orb) * (+1.0) +
1.0j * twist[0] *
(-1. + 2 * orb) * (-1.0))
factor_x_down_down = np.exp(-1.0j * twist[0] *
(-1. + 2 * orb) * (-1.0) +
1.0j * twist[0] *
(-1. + 2 * orb) * (-1.0))
if xi < xj:
factor_x_up_up = np.conj(factor_x_up_up)
factor_x_up_down = np.conj(factor_x_up_down)
factor_x_down_up = np.conj(factor_x_down_up)
factor_x_down_down = np.conj(factor_x_down_down)
if np.abs(yi - yj) > Ls // 2:
factor_y_up_up = np.exp(-1.0j * twist[1] *
(-1. + 2 * orb) * (+1.0) +
1.0j * twist[1] * (-1. + 2 * orb) *
(+1.0))
factor_y_up_down = np.exp(-1.0j * twist[1] *
(-1. + 2 * orb) * (-1.0) +
1.0j * twist[1] *
(-1. + 2 * orb) * (+1.0))
factor_y_down_up = np.exp(-1.0j * twist[1] *
(-1. + 2 * orb) * (+1.0) +
1.0j * twist[1] *
(-1. + 2 * orb) * (-1.0))
factor_y_down_down = np.exp(-1.0j * twist[1] *
(-1. + 2 * orb) * (-1.0) +
1.0j * twist[1] *
(-1. + 2 * orb) * (-1.0))
if yi < yj:
factor_y_up_up = np.conj(factor_y_up_up)
factor_y_up_down = np.conj(factor_y_up_down)
factor_y_down_up = np.conj(factor_y_down_up)
factor_y_down_down = np.conj(factor_y_down_down)
E_loc += edges_J[itotal, jtotal] * density(wf_state[2], itotal) * density(wf_state[2], jtotal) * \
factor_x_up_up * factor_y_up_up # s1 = s2
E_loc += edges_J[itotal, jtotal] * (1 - density(wf_state[2], itotal + L)) * (1 - density(wf_state[2], jtotal + L)) * \
factor_x_down_down * factor_y_down_down # s1 = s2
E_loc += -edges_J[itotal, jtotal] * get_wf_ratio_double_exchange(*wf_state, total_fugacity, itotal, jtotal + L, itotal + L, jtotal) * \
factor_x_up_down * factor_y_up_down
E_loc += -edges_J[itotal, jtotal] * get_wf_ratio_double_exchange(*wf_state, total_fugacity, jtotal, itotal + L, jtotal + L, itotal) * \
factor_x_down_up * factor_y_down_up
for mp in range(2):
iplus = i * 2 + mp
iminus = i * 2 + (1 - mp)
jplus = 2 * j + mp
jminus = j * 2 + (1 - mp)
_, _, xi, yi = from_linearized_index(iplus, Ls, n_orbitals,
n_sublattices)
_, _, xj, yj = from_linearized_index(jplus, Ls, n_orbitals,
n_sublattices)
factor_x_up_up = 1.0
factor_x_up_down = 1.0
factor_x_down_up = 1.0
factor_x_down_down = 1.0
factor_y_up_up = 1.0
factor_y_up_down = 1.0
factor_y_down_up = 1.0
factor_y_down_down = 1.0
if np.abs(xi - xj) > Ls // 2:
factor_x_up_up = np.exp(-1.0j * twist[0] * (-1. + 2 *
(1 - mp)) *
(+1.0) + 1.0j * twist[0] *
(-1. + 2 * mp) * (+1.0))
factor_x_up_down = np.exp(-1.0j * twist[0] * (-1. + 2 *
(1 - mp)) *
(-1.0) + 1.0j * twist[0] *
(-1. + 2 * mp) * (+1.0))
factor_x_down_up = np.exp(-1.0j * twist[0] * (-1. + 2 *
(1 - mp)) *
(+1.0) + 1.0j * twist[0] *
(-1. + 2 * mp) * (-1.0))
factor_x_down_down = np.exp(-1.0j * twist[0] * (-1. + 2 *
(1 - mp)) *
(-1.0) + 1.0j * twist[0] *
(-1. + 2 * mp) * (-1.0))
if xi < xj:
factor_x_up_up = np.conj(factor_x_up_up)
factor_x_up_down = np.conj(factor_x_up_down)
factor_x_down_up = np.conj(factor_x_down_up)
factor_x_down_down = np.conj(factor_x_down_down)
if np.abs(yi - yj) > Ls // 2:
factor_y_up_up = np.exp(-1.0j * twist[1] * (-1. + 2 *
(1 - mp)) *
(+1.0) + 1.0j * twist[1] *
(-1. + 2 * mp) * (+1.0))
factor_y_up_down = np.exp(-1.0j * twist[1] * (-1. + 2 *
(1 - mp)) *
(-1.0) + 1.0j * twist[1] *
(-1. + 2 * mp) * (+1.0))
factor_y_down_up = np.exp(-1.0j * twist[1] * (-1. + 2 *
(1 - mp)) *
(+1.0) + 1.0j * twist[1] *
(-1. + 2 * mp) * (-1.0))
factor_y_down_down = np.exp(-1.0j * twist[1] * (-1. + 2 *
(1 - mp)) *
(-1.0) + 1.0j * twist[1] *
(-1. + 2 * mp) * (-1.0))
if yi < yj:
factor_y_up_up = np.conj(factor_y_up_up)
factor_y_up_down = np.conj(factor_y_up_down)
factor_y_down_up = np.conj(factor_y_down_up)
factor_y_down_down = np.conj(factor_y_down_down)
E_loc += edges_J[iplus, jplus] * factor_x_up_up * factor_y_up_up * \
get_wf_ratio_double_exchange(*wf_state, total_fugacity, iplus, iminus, jminus, jplus) # up-up
E_loc += edges_J[iplus, jplus] * factor_x_down_down * factor_y_down_down * \
get_wf_ratio_double_exchange(*wf_state, total_fugacity, iminus + L, iplus + L, jplus + L, jminus + L) # down-down
E_loc += -edges_J[iplus, jplus] * factor_x_up_down * factor_y_up_down * \
get_wf_ratio_double_exchange(*wf_state, total_fugacity, iplus, jminus + L, iminus + L, jplus) # up-down
E_loc += -edges_J[iplus, jplus] * factor_x_down_up * factor_y_down_up * \
get_wf_ratio_double_exchange(*wf_state, total_fugacity, jminus, iplus + L, jplus + L, iminus) # down-up
return E_loc
def get_kinetic_orbitals(config, filling):
Ls = config.Ls
K0 = config.K_0
assert config.twist_mesh == 'PBC'
Tx, Ty = pairings.Tx_symmetry_map, pairings.Ty_symmetry_map
C3z = np.argmax(np.abs(pairings.C3z_symmetry_map_chiral), axis=0)
C2y = np.argmax(np.abs(pairings.C2y_symmetry_map_chiral), axis=0)
tx, ty = [], []
for i in range(Tx.shape[0]):
assert len(np.where(Tx[i, :] == 1)[0]) == 1
assert len(np.where(Ty[i, :] == 1)[0]) == 1
tx.append(np.where(Tx[i, :] == 1)[0][0])
ty.append(np.where(Ty[i, :] == 1)[0][0])
tx, ty = np.array(tx), np.array(ty)
np.save('tx.npy', tx)
np.save('ty.npy', ty)
assert np.allclose(tx[ty], ty[tx])
tx_valley = tx[::2] // 2
ty_valley = ty[::2] // 2
assert np.allclose(tx_valley[ty_valley], ty_valley[tx_valley])
valley = np.concatenate(
[np.array([2 * i + 1, 2 * i]) for i in range(config.Ls**2 * 2)])
path = '/home/astronaut/Documents/all_Imada_formats/'
########### writing the spin locations (none) ##########
f = open(os.path.join(path, 'locspn_{:d}.def'.format(Ls)), 'w')
f.write('================================\n')
f.write('NlocalSpin 0\n')
f.write('================================\n')
f.write('========i_0LocSpn_1IteElc ======\n')
f.write('================================\n')
for i in range(Ls**2 * 4):
f.write(' {:d} 0\n'.format(i))
f.close()
symmetries = [np.arange(Ls**2 * 4)]
########### writing the translational symmetries ##########
f = open(os.path.join(path, 'qptransidx_{:d}.def'.format(Ls)), 'w')
f.write('=============================================\n')
f.write('NQPTrans {:d}\n'.format(len(symmetries)))
f.write('=============================================\n')
f.write('======== TrIdx_TrWeight_and_TrIdx_i_xi ======\n')
f.write('=============================================\n')
for i in range(len(symmetries)):
f.write('{:d} 1.00000\n'.format(i))
for i, symm in enumerate(symmetries):
for i_from in range(symm.shape[0]):
f.write(' {:d} {:d} {:d}\n'.format(
i, i_from, symm[i_from]))
f.close()
from copy import deepcopy
########### writing the jastrows ##########
all_translations = [np.arange(Ls**2 * 4)]
curr_trans = tx.copy()
all_new_translations = []
for kx in range(config.Ls - 1):
new_translations = [symm[curr_trans] for symm in all_translations]
all_new_translations.append(deepcopy(new_translations))
curr_trans = curr_trans[tx]
for d in all_new_translations:
all_translations += d
curr_trans = ty.copy()
all_new_translations = []
for kx in range(config.Ls - 1):
new_translations = [symm[curr_trans] for symm in all_translations]
all_new_translations.append(deepcopy(new_translations))
curr_trans = curr_trans[ty]
for d in all_new_translations:
all_translations += d
f = open(os.path.join(path, 'jastrowidx_TRSbroken_{:d}.def'.format(Ls)),
'w')
jastrow_ij, jastrow_k, n_jastrows, matrix_jastrows = get_jastrow_fromshift(
all_translations,
config.Ls,
np.around(np.array(config.all_distances), decimals=5),
dist_threshold=5.)
np.save('check.npy', matrix_jastrows)
# G)
assert np.allclose(matrix_jastrows, matrix_jastrows.T)
matrix_jastrows_trans = matrix_jastrows.copy()
matrix_jastrows_trans = matrix_jastrows_trans[:, tx]
matrix_jastrows_trans = matrix_jastrows_trans[tx, :]
assert np.allclose(matrix_jastrows_trans, matrix_jastrows)
matrix_jastrows_trans = matrix_jastrows.copy()
matrix_jastrows_trans = matrix_jastrows_trans[:, ty]
matrix_jastrows_trans = matrix_jastrows_trans[ty, :]
assert np.allclose(matrix_jastrows_trans, matrix_jastrows)
f.write('=============================================\n')
f.write('NJastrowIdx {:d}\n'.format(n_jastrows + 1))
f.write('ComplexType {:d}\n'.format(0))
f.write('=============================================\n')
f.write('=============================================\n')
uniques = []
for i in range(config.Ls**2 * 4):
for j in range(config.Ls**2 * 4):
if i == j:
continue
f.write(' {:d} {:d} {:d}\n'.format(
i, j, matrix_jastrows[i, j]))
for i in range(n_jastrows + 1):
f.write(' {:d} 1\n'.format(i))
f.close()
f = open(os.path.join(path, 'InJastrow_TRSbroken_{:d}.def'.format(Ls)),
'w')
f.write('======================\n')
f.write('NJastrowIdx {:d}\n'.format(n_jastrows + 1))
f.write('======================\n')
f.write('== i_j_JastrowIdx ===\n')
f.write('======================\n')
for i in range(n_jastrows):
f.write('{:d} {:.10f} {:.10f}\n'.format(i, \
np.random.uniform(0.0, 1.0) * 0, np.random.uniform(0.0, 1.0) * 0))
f.write('{:d} {:.10f} {:.10f}\n'.format(n_jastrows, 0, 0))
f.close()
f = open(os.path.join(path, 'gutzwilleridx_{:d}.def'.format(Ls)), 'w')
f.write('=============================================\n')
f.write('NGutzwillerIdx {:d}\n'.format(1))
f.write('ComplexType {:d}\n'.format(0))
f.write('=============================================\n')
f.write('=============================================\n')
for i in range(4 * Ls**2):
f.write(' {:d} {:d}\n'.format(i, 0)) #idx))
for i in range(1):
f.write(' {:d} 1\n'.format(i))
f.close()
f = open(os.path.join(path, 'InGutzwiller.def'), 'w')
f.write('======================\n')
f.write('NGutzwillerIdx {:d}\n'.format(1))
f.write('======================\n')
f.write('== i_j_GutzwillerIdx ===\n')
f.write('======================\n')
for i in range(1):
f.write('{:d} {:.10f} {:.10f}\n'.format(
i,
np.random.uniform(0.0, 1.0) * 0,
np.random.uniform(0.0, 1.0) * 0))
f.close()
########### writing the modpara ##########
f = open(os.path.join(path, 'modpara_{:d}_{:d}.def'.format(Ls, filling)),
'w')
f.write('--------------------\n')
f.write('Model_Parameters 0\n')
f.write('--------------------\n')
f.write('VMC_Cal_Parameters\n')
f.write('--------------------\n')
f.write('CDataFileHead zvo\n')
f.write('CParaFileHead zqp\n')
f.write('--------------------\n')
f.write('NVMCCalMode 0\n')
f.write('--------------------\n')
f.write('NDataIdxStart 1\n')
f.write('NDataQtySmp 1\n')
f.write('--------------------\n')
f.write('Nsite {:d}\n'.format(Ls**2 * 4))
f.write('Ncond {:d}\n'.format(filling))
f.write('2Sz 0\n')
f.write('NSPGaussLeg 8\n')
f.write('NSPStot 0\n')
f.write('NMPTrans {:d}\n'.format(1))
f.write('NSROptItrStep 400\n')
f.write('NSROptItrSmp 40\n')
f.write('DSROptRedCut 0.0000001000\n')
f.write('DSROptStaDel 0.0200000000\n')
f.write('DSROptStepDt 0.0000020000\n')
f.write('NVMCWarmUp 400\n')
f.write('NVMCInterval 1\n')
f.write('NVMCSample 4000\n')
f.write('NExUpdatePath 0\n')
f.write('RndSeed 1\n')
f.write('NSplitSize 1\n')
f.write('NStore 0\n')
f.write('NSRCG 1\n')
f.close()
twist = (0, 0.5)
twist_exp = [
np.exp(2 * np.pi * 1.0j * twist[0]),
np.exp(2 * np.pi * 1.0j * twist[1])
]
fft = get_fft_APBCy(config.Ls)
for gap_idx in [40, 9, 36, 14]:
#[0, 32, 43, 17, 11, 19]: # 40, 43, 9, 36[!!]
print('gap_idx = ', gap_idx)
#if config.idx_map[gap_idx] != 13:
# continue
for gap_val in [0.0, 0.003, 0.02]:
#g = gap_val * np.load('the_wave_extended_{:d}.npy'.format(config.Ls))
g = gap_val * np.load(
'/home/astronaut/Documents/DQMC_TBG/gaps_8x8/gap_{:d}.npy'.
format(gap_idx))
# = gap_val * np.load('/home/astronaut/Documents/XQMC/gaps_6x6_extended/twist_0/gap_{:d}.npy'.format(gap_idx))
#gap_val * np.load('/home/astronaut/Documents/DQMC_TBG/gaps_8x8/gap_{:d}.npy'.format(gap_idx))
if config.Ls == 6:
g = models.xy_to_chiral(g, 'pairing', config, True)
TRS = np.concatenate(
[np.array([2 * i + 1, 2 * i]) for i in range(g.shape[0] // 2)])
g_TRS = g[:, TRS]
g_TRS = g_TRS[TRS, :]
g = g + g_TRS # * (0.1 if gap_val == 0.02 else 1.)
#np.save('sheck.npy', g)
if gap_idx in [11, 19]:
g = g / 1.0j
# g = (g + g.conj()) / np.sqrt(2)
print(g[0], 'g[0]')
print(g[1], 'g[1]')
assert np.allclose(g, g.T)
swave = 1e-5 * models.xy_to_chiral(
pairings.combine_product_terms(
config, pairings.twoorb_hex_all[1]), 'pairing', config,
True)
assert np.allclose(swave, swave.T)
print(swave[0], swave[1], 'swave in chiral basis')
g = g + swave
gap = models.apply_TBC(config,
twist_exp,
deepcopy(g),
inverse=False)
#np.save('the_wave_extended_twisted_{:d}.npy'.format(config.Ls), models.apply_TBC(config, twist_exp, deepcopy(np.load('the_wave_extended_{:d}.npy'.format(config.Ls))), inverse = False))
#exit(-1)
gapT = models.apply_TBC(config,
twist_exp,
deepcopy(g).T,
inverse=True)
gap_fft = fft.T.conj().dot(gap).dot(fft)
gap_check = gap_fft.copy()
for i in range(gap_check.shape[0] // 4):
#print(i % 4, i // 4)
#(np.abs(np.linalg.eig(gap_check[i * 4:i * 4 + 4,i * 4:i * 4 + 4])[0]), i)
# print(gap_check[i * 4:i * 4 + 4,i * 4:i * 4 + 4])
#assert np.allclose(gap_check[i * 4:i * 4 + 4,i * 4:i * 4 + 4], gap_check[i * 4:i * 4 + 4,i * 4:i * 4 + 4].conj().T)
gap_check[i * 4:i * 4 + 4, i * 4:i * 4 + 4] = 0.0
assert np.isclose(np.sum(np.abs(gap_check)), 0.0)
############ determine required mu_BCS to start ################
K0_up = models.apply_TBC(config,
twist_exp,
deepcopy(K0),
inverse=False)
K0_down = models.apply_TBC(config,
twist_exp,
deepcopy(K0),
inverse=True)
K0_downT = models.apply_TBC(config,
twist_exp,
deepcopy(K0),
inverse=True).T
K0_upT = models.apply_TBC(config,
twist_exp,
deepcopy(K0),
inverse=False).T
#print('energies {:d}'.format(config.Ls), np.linalg.eigh(K0_up)[0])
#exit(-1)
#### check twist is correct ###
K0_fft_plus = fft.conj().T.dot(K0_up).dot(fft)
K0_fft_minus = fft.T.dot(K0_up).dot(fft.conj())
K0_check = K0_fft_plus.copy()
for i in range(K0_check.shape[0] // 4):
K0_check[i * 4:i * 4 + 4, i * 4:i * 4 + 4] = 0.0
assert np.isclose(np.sum(np.abs(K0_check)), 0.0)
K0_check = K0_fft_minus.copy()
for i in range(K0_check.shape[0] // 4):
K0_check[i * 4:i * 4 + 4, i * 4:i * 4 + 4] = 0.0
assert np.isclose(np.sum(np.abs(K0_check)), 0.0)
assert np.allclose(K0_up, K0_up.conj().T)
assert np.allclose(K0_down, K0_down.conj().T)
L = K0.shape[0]
totalM = np.zeros((4 * L, 4 * L), dtype=np.complex128)
totalM[:L, :L] = K0_up
totalM[L:2 * L, L:2 * L] = K0_down
totalM[2 * L:3 * L, 2 * L:3 * L] = -K0_upT
totalM[3 * L:, 3 * L:] = -K0_downT
totalM[:L, 3 * L:] = gap
totalM[L:2 * L, 2 * L:3 * L] = -gapT
totalM[2 * L:3 * L, L:2 * L] = -gapT.conj().T
totalM[3 * L:, :L] = gap.conj().T
energies = np.linalg.eigh(totalM)[
0] # energies with BC twist and gap
#print(energies)
mu_BCS = (energies[filling * 2] + energies[filling * 2 - 1]) / 2.
print(energies[filling * 2], energies[filling * 2 - 1])
#assert not np.isclose(energies[filling * 2], energies[filling * 2 - 1])
print('mu_BCS = ', mu_BCS)
K0_up = K0_up - np.eye(K0_up.shape[0]) * mu_BCS
K0_upT = K0_upT - np.eye(K0_upT.shape[0]) * mu_BCS
K0_down = K0_down - np.eye(K0_down.shape[0]) * mu_BCS
K0_downT = K0_downT - np.eye(K0_downT.shape[0]) * mu_BCS
L = K0.shape[0]
totalM = np.zeros((4 * L, 4 * L), dtype=np.complex128)
totalM[:L, :L] = K0_up
totalM[L:2 * L, L:2 * L] = K0_down
totalM[2 * L:3 * L, 2 * L:3 * L] = -K0_upT
totalM[3 * L:, 3 * L:] = -K0_downT
totalM[:L, 3 * L:] = gap
totalM[L:2 * L, 2 * L:3 * L] = -gapT
totalM[2 * L:3 * L, L:2 * L] = -gapT.conj().T
totalM[3 * L:, :L] = gap.conj().T
selected_idxs = np.concatenate(
[np.arange(0, L), np.arange(3 * L, 4 * L)])
totalM_updown = totalM[:, selected_idxs]
totalM_updown = totalM_updown[selected_idxs, ...]
#totalM_updown = np.zeros((2 * L, 2 * L), dtype=np.complex128)
#totalM_updown[:L, :L] = K0; totalM_updown[L:, L:] = -K0.T;
#totalM_updown[:L, L:] = gap; totalM_updown[L:, :L] = gap.conj().T;
selected_idxs = np.arange(L, 3 * L)
totalM_downup = totalM[:, selected_idxs]
totalM_downup = totalM_downup[selected_idxs, ...]
TRS = np.concatenate([
np.array([2 * i + 1, 2 * i], dtype=np.int64) for i in range(L)
])
#totalM_downup = np.zeros((2 * L, 2 * L), dtype=np.complex128)
#totalM_downup[:L, :L] = K0; totalM_downup[L:, L:] = -K0.T;
#totalM_downup[:L, L:] = -gap.T; totalM_downup[L:, :L] = -gap.conj();
en_updown, W_updown = np.linalg.eigh(totalM_updown)
totalM_updown_TRS = totalM_updown[TRS, ...]
totalM_updown_TRS = totalM_updown_TRS[..., TRS]
totalM_updown_TRS = totalM_updown_TRS.conj()
print('after TRS, discrepancy',
np.sum(np.abs(totalM_updown_TRS - totalM_updown)))
en_downup, W_downup = np.linalg.eigh(totalM_downup)
assert np.allclose(en_updown, np.sort(-en_updown))
assert np.allclose(en_downup, np.sort(-en_downup))
en_total, W = np.linalg.eigh(totalM)
#print('energies with gap', gap_val, en_total)
#print('updown energies', en_updown)
#print('downup energies', en_downup)
#for en, state in zip(en_downup, W_downup.T):
# if np.abs(en + 0.03085819) < 1e-6:
# print(en, state)
#exit(-1)
for i in range(W_updown.shape[1] // 2):
v = W_updown[:, i]
en = en_updown[i]
v_conj = v * 0.0
v_conj[:len(v) // 2] = v[len(v) // 2:].conj()
v_conj[len(v) // 2:] = v[:len(v) // 2].conj()
en_conj = np.dot(v_conj.conj(),
totalM_updown.dot(v_conj)) / np.dot(
v_conj.conj(), v_conj)
#print(en_conj, en, np.dot(v_conj.conj(), v_conj), np.dot(v.conj(), totalM_updown.dot(v)))
#W_conj.append(v_conj)
#assert np.isclose(en_conj, -en)
#exit(-1)
W_conj = []
for i in range(W.shape[1] // 2):
v = W[:, i]
en = en_total[i]
v_conj = v * 0.0
v_conj[:len(v) // 2] = v[len(v) // 2:].conj()
v_conj[len(v) // 2:] = v[:len(v) // 2].conj()
en_conj = np.dot(v_conj.conj(), totalM.dot(v_conj))
#print(en_conj, en)
W_conj.append(v_conj)
assert np.isclose(en_conj, -en)
W_conj = np.array(W_conj).T
W[:, W.shape[1] //
2:] = W_conj # make the right form -- but this makes no difference: this is only rearrangement of 2nd part of the array, while we only use the 1st part
# why W does not protect that block form? -- or do we even need this form?
assert np.allclose(
np.diag(W.conj().T.dot(totalM).dot(W)).real,
np.diag(W.conj().T.dot(totalM).dot(W)))
assert np.allclose(
np.sort(np.diag(W.conj().T.dot(totalM).dot(W)).real),
np.linalg.eigh(totalM)[0])
# with gap 6, W_pieces does not diagonalize totalM! why?
W_pieces = np.zeros((4 * L, 4 * L), dtype=np.complex128)
W_pieces[:L, :L] = W_updown[:L, :L]
W_pieces[3 * L:, 3 * L:] = W_updown[L:, L:]
W_pieces[3 * L:, :L] = W_updown[L:, :L]
W_pieces[:L, 3 * L:] = W_updown[:L, L:]
W_pieces[L:2 * L, L:2 * L] = W_downup[:L, :L]
W_pieces[2 * L:3 * L, 2 * L:3 * L] = W_downup[L:, L:]
W_pieces[2 * L:3 * L, L:2 * L] = W_downup[L:, :L]
W_pieces[L:2 * L, 2 * L:3 * L] = W_downup[:L, L:]
#assert np.allclose(np.sort(np.diag(W_pieces.conj().T.dot(totalM).dot(W_pieces)).real), np.sort(np.diag(W_pieces.conj().T.dot(totalM).dot(W_pieces))))
#assert np.isclose(np.sum(np.abs(W_pieces.conj().T.dot(totalM).dot(W_pieces) - np.diag(np.diag(W_pieces.conj().T.dot(totalM).dot(W_pieces))))), 0.0)
assert np.isclose(
np.sum(
np.abs(W.conj().T.dot(totalM).dot(W) -
np.diag(np.diag(W.conj().T.dot(totalM).dot(W))))),
0.0)
#print(np.sort(np.diag(W.conj().T.dot(totalM).dot(W)).real) - np.sort(np.diag(W_pieces.conj().T.dot(totalM).dot(W_pieces)).real))
#assert np.allclose(np.sort(np.diag(W.conj().T.dot(totalM).dot(W)).real), \
# np.sort(np.diag(W_pieces.conj().T.dot(totalM).dot(W_pieces)).real))
#print(np.linalg.det(W_updown), np.linalg.det(W_downup), np.linalg.det(W_updown) * np.linalg.det(W_downup))
#print(np.linalg.det(W_pieces))
#print(np.linalg.det(W))
for i in range(W_updown.shape[1]):
v = W_updown[:, i]
en = en_updown[i]
v_conj = v * 0.0
v_conj[:len(v) // 2] = v[len(v) // 2:].conj()
v_conj[len(v) // 2:] = v[:len(v) // 2].conj()
en_conj = np.dot(v_conj.conj(), totalM_updown.dot(v_conj))
# print(en_conj, en)
#assert en_conj == -en
mask = np.zeros((4 * L, 4 * L), dtype=np.complex128)
mask[:L, :L] = np.ones((L, L))
mask[L:2 * L, L:2 * L] = np.ones((L, L))
mask[2 * L:3 * L, 2 * L:3 * L] = np.ones((L, L))
mask[3 * L:, 3 * L:] = np.ones((L, L))
mask[3 * L:, :L] = np.ones((L, L))
mask[2 * L:3 * L, L:2 * L] = np.ones((L, L))
mask[L:2 * L, 2 * L:3 * L] = np.ones((L, L))
mask[:L, 3 * L:] = np.ones((L, L))
#totalM[:L, :L] = K0; totalM[L:2 * L, L:2 * L] = K0; totalM[2 * L:3 * L, 2 * L:3 * L] = -K0.T; totalM[3 * L:, 3 * L:] = -K0.T
#totalM[:L, 2 * L:3 * L] = gap; totalM[L: 2 * L, 3 * L:] = -gap.T; totalM[3 * L:, L: 2 * L] = -gap.conj(); totalM[2 * L:3 * L, :L] = gap.conj().T;
assert np.allclose(totalM, totalM.conj().T)
# W = np.linalg.eigh(totalM / 2.)[1]
#print(np.linalg.eigh(totalM / 2.)[0])
#assert np.sum(np.abs(W - W * mask)) == 0
#assert np.allclose(W[:W.shape[0] // 2, :W.shape[0] // 2], W[W.shape[0] // 2:, W.shape[0] // 2:].conj())
#assert np.allclose(W[W.shape[0] // 2:, :W.shape[0] // 2], W[:W.shape[0] // 2, W.shape[0] // 2:].conj())
Q, V = W[:W.shape[0] // 2, :W.shape[0] // 2], \
W[W.shape[0] // 2:, :W.shape[0] // 2]
Z = (Q.dot(np.linalg.inv(V)))
print('max U^{-1} = ', np.max(np.abs(np.linalg.inv(Q))), gap_val,
gap_idx)
np.save('Z_fast.npy', Z)
result = Z[Z.shape[0] // 2:, :Z.shape[0] // 2]
Z = Z / np.max(np.abs(Z))
print(
np.sum(
np.abs(Z[Z.shape[0] // 2:, :Z.shape[0] // 2] +
Z[:Z.shape[0] // 2, Z.shape[0] // 2:].T)))
print(
np.sum(
np.abs(
np.real(Z[Z.shape[0] // 2:, :Z.shape[0] // 2] +
Z[:Z.shape[0] // 2, Z.shape[0] // 2:].T))))
print(
np.sum(
np.abs(
np.imag(Z[Z.shape[0] // 2:, :Z.shape[0] // 2] +
Z[:Z.shape[0] // 2, Z.shape[0] // 2:].T))))
assert np.allclose(Z[Z.shape[0] // 2:, :Z.shape[0] // 2],
-Z[:Z.shape[0] // 2, Z.shape[0] // 2:].T)
assert np.allclose(Z[Z.shape[0] // 2:, Z.shape[0] // 2:],
Z[Z.shape[0] // 2:, Z.shape[0] // 2:] * 0.0)
assert np.allclose(Z[:Z.shape[0] // 2, :Z.shape[0] // 2],
Z[:Z.shape[0] // 2, :Z.shape[0] // 2] * 0.0)
##### preparing orbital idxs and teir initial values ####
vol = 4 * Ls**2
orbital_idxs = -np.ones((vol, vol), dtype=np.int64)
f_ij = result
f_ij = f_ij / np.abs(np.max(f_ij))
np.save('f_ij_fast.npy', f_ij)
current_orb_idx = 0
for xshift in range(Ls):
for yshift in range(Ls):
for iorb in range(4):
for jorb in range(4):
if yshift > 0:
for ipos in range(Ls**2):
i = ipos * 4 + iorb
oi, si, xi, yi = models.from_linearized_index(
i, config.Ls, config.n_orbitals,
config.n_sublattices)
j = models.to_linearized_index(
(xi + xshift) % Ls, (yi + yshift) % Ls,
jorb % 2, jorb // 2, Ls, 2, 2)
if yi + yshift > Ls - 1:
orbital_idxs[i, j] = current_orb_idx
current_orb_idx += 1
for ipos in range(Ls**2):
i = ipos * 4 + iorb
oi, si, xi, yi = models.from_linearized_index(
i, config.Ls, config.n_orbitals,
config.n_sublattices)
j = models.to_linearized_index(
(xi + xshift) % Ls, (yi + yshift) % Ls,
jorb % 2, jorb // 2, Ls, 2, 2)
if yi + yshift <= Ls - 1:
orbital_idxs[i, j] = current_orb_idx
current_orb_idx += 1
print('FAST: orbitals after enforcing APBCy remaining:',
current_orb_idx)
for i in range(current_orb_idx):
values = f_ij.flatten()[orbital_idxs.flatten() == i]
assert np.isclose(np.std(values - values.mean()), 0.0)
if np.allclose(f_ij, f_ij.T):
print(
'FAST: symmetric f_ij = f_ji (singlet): restricting su(2) parameters'
)
for i in range(vol):
for j in range(vol):
orb_ij = orbital_idxs[i, j]
orb_ji = orbital_idxs[j, i]
orbital_idxs[i, j] = np.min([orb_ij, orb_ji])
orbital_idxs[j, i] = np.min([orb_ij, orb_ji])
new_orbitals = np.unique(orbital_idxs.flatten())
mapping = list(np.sort(new_orbitals))
for i in range(vol):
for j in range(vol):
orbital_idxs[i, j] = mapping.index(orbital_idxs[i, j])
for i in range(len(mapping)):
values = f_ij.flatten()[orbital_idxs.flatten() == i]
assert np.isclose(np.std(values - values.mean()), 0.0)
print('FAST: total orbitals su(2) with APBCy', len(mapping))
current_orb_idx = len(mapping)
TRS = np.concatenate([[2 * i + 1, 2 * i] for i in range(vol // 2)])
f_trs = f_ij[:, TRS]
f_trs = f_trs[TRS, :]
if np.allclose(f_trs, f_ij):
print('FAST: f_ij = TRS f_ij: resticting TRS parameters')
for i in range(vol):
for j in range(vol):
orb_ij = orbital_idxs[i, j]
i_trs = ((i // 2) * 2) + (((i % 2) + 1) % 2)
j_trs = ((j // 2) * 2) + (((j % 2) + 1) % 2)
orb_ij_trs = orbital_idxs[i_trs, j_trs]
#print(f_ij[i, j], f_ij[i_trs, j_trs])
assert np.isclose(f_ij[i, j], f_ij[i_trs, j_trs])
orbital_idxs[i, j] = np.min([orb_ij, orb_ij_trs])
orbital_idxs[i_trs,
j_trs] = np.min([orb_ij, orb_ij_trs])
#for i in range(current_orb_idx):
# if np.sum(orbital_idxs.flatten() == i) == 0:
# print('orbital', i, 'is missing')
new_orbitals = np.unique(orbital_idxs.flatten())
mapping = list(np.sort(new_orbitals))
for i in range(vol):
for j in range(vol):
orbital_idxs[i, j] = mapping.index(orbital_idxs[i, j])
for i in range(len(mapping)):
values = f_ij.flatten()[orbital_idxs.flatten() == i]
assert np.isclose(np.std(values - values.mean()), 0.0)
print('FAST: total orbitals su(2) with APBCy and TRS!',
len(mapping) + 1)
current_orb_idx = len(mapping)
np.save('orbital_idxs_fast.npy', orbital_idxs)
f = open(
os.path.join(
path,
'InOrbital_extended_{:d}_{:d}_{:d}_{:.4f}.def'.format(
Ls, gap_idx, filling, gap_val)), 'w')
f.write('======================\n')
f.write('NOrbitalIdx {:d}\n'.format(current_orb_idx))
f.write('======================\n')
f.write('== i_j_OrbitalIdx ===\n')
f.write('======================\n')
for k in range(current_orb_idx):
mask = (orbital_idxs == k)
val = np.sum(f_ij * mask) / np.sum(mask)
f.write('{:d} {:.20f} {:.20f}\n'.format(
k, val.real, val.imag))
f.close()
########### writing the orbitals indexes ##########
f = open(
os.path.join(
path, 'orbitalidx_extended_{:d}_{:d}_{:d}.def'.format(
Ls, gap_idx, filling)), 'w')
f.write('=============================================\n')
f.write('NOrbitalIdx {:d}\n'.format(current_orb_idx))
f.write('ComplexType {:d}\n'.format(1))
f.write('=============================================\n')
f.write('=============================================\n')
for i in range(config.Ls**2 * 4):
for j in range(config.Ls**2 * 4):
f.write(' {:d} {:d} {:d}\n'.format(
i, j, orbital_idxs[i, j]))
for i in range(current_orb_idx):
f.write(' {:d} 1\n'.format(i))
f.close()
twist_exp = [
np.exp(2.0j * np.pi * twist[0]),
np.exp(2.0j * np.pi * twist[1])
]
K_0_twisted = models.apply_TBC(config,
twist_exp,
deepcopy(K0),
inverse=False)
########### writing the K--matrix ##########
K0_up_int = K0_up - np.diag(np.diag(K0_up))
K0_down_int = K0_down - np.diag(np.diag(K0_down))
f = open(
os.path.join(path,
'trans_{:d}_{:.3f}_{:.3f}.def'.format(Ls,
*twist)),
'w')
f.write('========================\n')
f.write('NTransfer {:d}\n'.format(
2 * np.sum(np.abs(K0_up_int) > 1e-7)))
f.write('========================\n')
f.write('========i_j_s_tijs======\n')
f.write('========================\n')
for i in range(K_0_twisted.shape[0]):
for j in range(K_0_twisted.shape[1]):
if np.abs(K0_up_int[i, j]) > 1e-7:
f.write(
' {:d} 0 {:d} 0 {:.6f} {:.6f}\n'.
format(i, j, np.real(-K0_up_int[i, j]),
np.imag(-K0_up_int[i, j])))
f.write(
' {:d} 1 {:d} 1 {:.6f} {:.6f}\n'.
format(i, j, np.real(-K0_down_int[i, j]),
np.imag(-K0_down_int[i, j])))
f.close()
return
def plot_Jastrow(config, Jastrow, index):
geometry = 'hexagonal' if config.n_sublattices == 2 else 'square'
pairing, name = Jastrow
if geometry == 'hexagonal':
R = models.R_hexagonal
else:
R = models.R_square
set_style()
textshift = np.array([0.1, 0.1])
x1, y1 = config.Ls // 2, config.Ls // 2
for sublattice1 in range(config.n_sublattices):
for orbit1 in range(config.n_orbitals):
first = models.to_linearized_index(x1, y1, sublattice1, orbit1,
config.Ls, config.n_orbitals,
config.n_sublattices)
for second in range(config.total_dof // 2):
orbit2, sublattice2, x2, y2 = models.from_linearized_index(deepcopy(second), config.Ls, \
config.n_orbitals, config.n_sublattices)
if pairing[first, second] == 0:
continue
value = 1.
labelstring = str(value)
labelstring = '(' + str(orbit1) + '-' + str(
orbit2) + '), ' + labelstring + ' ' + str(index)
r1 = np.array([x1, y1]).dot(R) + sublattice1 * np.array(
[1, 0]) / np.sqrt(3) # always 0 in the square case
r2 = np.array([
x2, y2
]).dot(R) + sublattice2 * np.array([1, 0]) / np.sqrt(3)
r1_origin = np.array([x1, y1]).dot(R)
r1 = r1 - r1_origin
r2 = r2 - r1_origin
if sublattice2 == 0:
plt.scatter(*r2, s=20, color='red')
else:
plt.scatter(*r2, s=20, color='blue')
if np.sum(np.abs(r1 - r2)) < 1e-5:
plt.plot([r1[0]], [r1[1]], marker='*', ms=10)
else:
plt.annotate(s='',
xy=r2,
xytext=r1,
arrowprops=dict(arrowstyle='->'))
textshift = np.array([r2[1] - r1[1], r1[0] - r2[0]])
textshift = textshift / np.sqrt(np.sum(textshift**2) + 1e-5)
shiftval = 0.1 - (orbit1 * config.n_orbitals +
orbit2) * 0.1 / 2
plt.text(*(r2 + shiftval * textshift +
np.random.uniform(-0.05, 0.05, 2)),
labelstring,
zorder=10,
fontsize=8)
plt.xlabel('$x$')
plt.ylabel('$y$')
plt.title(name)
plt.savefig('../plots/' + name + '.pdf')
plt.clf()
return
def plot_wave(config, wave, name):
geometry = 'hexagonal' if config.n_sublattices == 2 else 'square'
if geometry == 'hexagonal':
R = models.R_hexagonal
else:
R = models.R_square
set_style()
textshift = np.array([0.1, 0.1])
x1, y1 = config.Ls // 2, config.Ls // 2
for sublattice1 in range(config.n_sublattices):
for orbit1 in range(config.n_orbitals):
first = models.to_linearized_index(x1, y1, sublattice1, orbit1,
config.Ls, config.n_orbitals,
config.n_sublattices)
for second in range(config.total_dof // 2):
orbit2, sublattice2, x2, y2 = models.from_linearized_index(deepcopy(second), config.Ls, \
config.n_orbitals, config.n_sublattices)
if wave[first, second] == 0:
continue
value_uu = wave[first, second]
value_dd = wave[first + config.total_dof // 2,
second + config.total_dof // 2]
labelstring_up = str(value_uu)
if np.abs(value_uu.imag) < 1e-10:
labelstring_up = str(value_uu.real)
elif geometry == 'hexagonal':
if np.abs(value_uu -
np.exp(2.0 * np.pi / 3.0 * 1.0j)) < 1e-11:
labelstring_up = '$\\omega$'
if np.abs(value_uu +
np.exp(2.0 * np.pi / 3.0 * 1.0j)) < 1e-11:
labelstring_up = '$-\\omega$'
if np.abs(value_uu -
np.exp(-2.0 * np.pi / 3.0 * 1.0j)) < 1e-11:
labelstring_up = '$\\omega^*$'
if np.abs(value_uu +
np.exp(-2.0 * np.pi / 3.0 * 1.0j)) < 1e-11:
labelstring_up = '$-\\omega^*$'
if np.abs(value_uu -
1.0j * np.exp(2.0 * np.pi / 3.0 * 1.0j)) < 1e-11:
labelstring_up = '$i \\omega$'
if np.abs(value_uu +
1.0j * np.exp(2.0 * np.pi / 3.0 * 1.0j)) < 1e-11:
labelstring_up = '$-i \\omega$'
if np.abs(value_uu - 1.0j *
np.exp(-2.0 * np.pi / 3.0 * 1.0j)) < 1e-11:
labelstring_up = '$i \\omega^*$'
if np.abs(value_uu + 1.0j *
np.exp(-2.0 * np.pi / 3.0 * 1.0j)) < 1e-11:
labelstring_up = '$-i \\omega^*$'
if np.abs(value_uu - 1.0j) < 1e-7:
labelstring_up = '$i$'
if np.abs(value_uu + 1.0j) < 1e-7:
labelstring_up = '$-i$'
if np.abs(value_uu - 1.0) < 1e-7:
labelstring_up = '$1$'
if np.abs(value_uu + 1.0) < 1e-7:
labelstring_up = '$-1$'
if np.abs(value_uu - 1.0j * np.sqrt(3)) < 1e-7:
labelstring_up = '$i\\sqrt{3}$'
if np.abs(value_uu + 1.0j * np.sqrt(3)) < 1e-7:
labelstring_up = '$-i\\sqrt{3}$'
if np.abs(value_uu - np.sqrt(3)) < 1e-7:
labelstring_up = '$\\sqrt{3}$'
if np.abs(value_uu + np.sqrt(3)) < 1e-7:
labelstring_up = '$-\\sqrt{3}$'
labelstring_up = '(' + str(orbit1) + '-' + str(
orbit2) + '), ' + labelstring_up + ', $\\uparrow$'
labelstring_down = str(value_dd)
if np.abs(value_dd.imag) < 1e-10:
labelstring_down = str(value_dd.real)
elif geometry == 'hexagonal':
if np.abs(value_dd -
np.exp(2.0 * np.pi / 3.0 * 1.0j)) < 1e-11:
labelstring_down = '$\\omega$'
if np.abs(value_dd +
np.exp(2.0 * np.pi / 3.0 * 1.0j)) < 1e-11:
labelstring_down = '$-\\omega$'
if np.abs(value_dd -
np.exp(-2.0 * np.pi / 3.0 * 1.0j)) < 1e-11:
labelstring_down = '$\\omega^*$'
if np.abs(value_dd +
np.exp(-2.0 * np.pi / 3.0 * 1.0j)) < 1e-11:
labelstring_down = '$-\\omega^*$'
if np.abs(value_dd -
1.0j * np.exp(2.0 * np.pi / 3.0 * 1.0j)) < 1e-11:
labelstring_down = '$i \\omega$'
if np.abs(value_dd +
1.0j * np.exp(2.0 * np.pi / 3.0 * 1.0j)) < 1e-11:
labelstring_down = '$-i \\omega$'
if np.abs(value_dd - 1.0j *
np.exp(-2.0 * np.pi / 3.0 * 1.0j)) < 1e-11:
labelstring_down = '$i \\omega^*$'
if np.abs(value_dd + 1.0j *
np.exp(-2.0 * np.pi / 3.0 * 1.0j)) < 1e-11:
labelstring_down = '$-i \\omega^*$'
if np.abs(value_dd - 1.0j) < 1e-7:
labelstring_down = '$i$'
if np.abs(value_dd + 1.0j) < 1e-7:
labelstring_down = '$-i$'
if np.abs(value_dd - 1.0) < 1e-7:
labelstring_down = '$1$'
if np.abs(value_dd + 1.0) < 1e-7:
labelstring_down = '$-1$'
if np.abs(value_dd - 1.0j * np.sqrt(3)) < 1e-7:
labelstring_down = '$i\\sqrt{3}$'
if np.abs(value_dd + 1.0j * np.sqrt(3)) < 1e-7:
labelstring_down = '$-i\\sqrt{3}$'
if np.abs(value_dd - np.sqrt(3)) < 1e-7:
labelstring_down = '$\\sqrt{3}$'
if np.abs(value_dd + np.sqrt(3)) < 1e-7:
labelstring_down = '$-\\sqrt{3}$'
labelstring_down = '(' + str(orbit1) + '-' + str(
orbit2) + '), ' + labelstring_down + ', $\\downarrow$'
r1 = np.array([x1, y1]).dot(R) + sublattice1 * np.array(
[1, 0]) / np.sqrt(3) # always 0 in the square case
r2 = np.array([
x2, y2
]).dot(R) + sublattice2 * np.array([1, 0]) / np.sqrt(3)
r1_origin = np.array([x1, y1]).dot(R)
r1 = r1 - r1_origin
r2 = r2 - r1_origin
if sublattice2 == 0:
plt.scatter(*r2, s=20, color='red')
else:
plt.scatter(*r2, s=20, color='blue')
plt.annotate(s='',
xy=r2,
xytext=r1,
arrowprops=dict(arrowstyle='->'))
textshift = np.array([r2[1] - r1[1], r1[0] - r2[0]])
textshift = textshift / np.sqrt(np.sum(textshift**2) + 1e-5)
shiftval = 0.4 - (
(orbit1 * config.n_orbitals + orbit2) + 4) * 0.1
plt.text(*(r2 + np.random.uniform(-0.003, 0.003, size=2) +
shiftval * textshift),
labelstring_up,
zorder=10,
fontsize=8,
color='orange')
shiftval = 0.4 - ((orbit1 * config.n_orbitals + orbit2)) * 0.1
plt.text(*(r2 + np.random.uniform(-0.003, 0.003, size=2) +
shiftval * textshift),
labelstring_down,
zorder=10,
fontsize=8,
color='violet')
plt.xlabel('$x$')
plt.ylabel('$y$')
#plt.xlim([-0.5, 1.25])
#plt.ylim([-0.75, 0.75])
# plt.title(name + ' pairing')
plt.savefig('../plots/' + name + '.pdf')
plt.clf()
return
