def test_full_symm_3byb3(self):
U = 20 * (np.random.rand() - 0.5)
t = np.random.rand()
gm = geom.Geometry.createSquareGeometry(3,
3,
0,
0,
bc1_open=False,
bc2_open=False)
model = ed_fermions.fermions(gm, U, t, ns=np.array([2, 2]))
# no symmetry
hamiltonian_full = model.createH(projector=model.n_projector)
eig_vals_full, eig_vects_full = model.diagH(hamiltonian_full)
# rotational symmetry
cx, cy = model.geometry.get_center_of_mass()
rot_fn = symm.getRotFn(4, cx=cx, cy=cy)
rot_cycles, max_cycle_len_rot = symm.findSiteCycles(
rot_fn, model.geometry)
rot_op = model.n_projector.dot(
model.get_xform_op(rot_cycles).dot(
model.n_projector.conj().transpose()))
# reflection symmetry
refl_fn = symm.getReflFn(np.array([[0], [1]]), cx=cx, cy=cy)
refl_cycles, max_cycle_len_refl = symm.findSiteCycles(
refl_fn, model.geometry)
refl_op = model.n_projector.dot(
model.get_xform_op(refl_cycles).dot(
model.n_projector.conj().transpose()))
# translational symmetry
tx_fn = symm.getTranslFn(np.array([[1], [0]]))
tx_cycles, tx_max = symm.findSiteCycles(tx_fn, model.geometry)
tx_op_full = model.get_xform_op(tx_cycles)
tx_op = model.n_projector.dot(
tx_op_full.dot(model.n_projector.conj().transpose()))
ty_fn = symm.getTranslFn((np.array([[0], [1]])))
ty_cycles, ty_max = symm.findSiteCycles(ty_fn, model.geometry)
ty_op_full = model.get_xform_op(ty_cycles)
ty_op = model.n_projector.dot(
ty_op_full.dot(model.n_projector.conj().transpose()))
symm_projs = symm.getC4V_and_3byb3(rot_op, refl_op, tx_op, ty_op)
eig_vals_sectors = []
for ii, proj in enumerate(symm_projs):
h_sector = model.createH(projector=proj.dot(model.n_projector))
eig_vals_sector, eig_vects_sector = model.diagH(h_sector)
eig_vals_sectors.append(eig_vals_sector)
# why only accurate to 10 decimal places?
eigs_all_sectors = np.sort(np.concatenate(eig_vals_sectors))
max_diff = np.abs(eig_vals_full - eigs_all_sectors).max()
self.assertAlmostEqual(max_diff, 0, 10)
def test_translational_symm_3x3(self):
"""
Test translational symmetry by diagonalizing random 3x3 spin system with and without it
:return:
"""
cluster = geom.Geometry.createSquareGeometry(3,
3,
0,
0,
bc1_open=False,
bc2_open=False)
jx = np.random.rand()
jy = np.random.rand()
jz = np.random.rand()
hx = np.random.rand()
hy = np.random.rand()
hz = np.random.rand()
# diagonalize full hamiltonian
spin_model = tvi.spinSystem(cluster,
jx,
jy,
jz,
hx,
hy,
hz,
use_ryd_detunes=0)
hamiltonian_full = spin_model.createH()
eig_vals_full, eig_vects_full = spin_model.diagH(hamiltonian_full)
xtransl_fn = symm.getTranslFn(np.array([[1], [0]]))
xtransl_cycles, max_cycle_len_translx = symm.findSiteCycles(
xtransl_fn, spin_model.geometry)
xtransl_op = spin_model.get_xform_op(xtransl_cycles)
xtransl_op = xtransl_op
# y-translations
ytransl_fn = symm.getTranslFn(np.array([[0], [1]]))
ytransl_cycles, max_cycle_len_transly = symm.findSiteCycles(
ytransl_fn, spin_model.geometry)
ytransl_op = spin_model.get_xform_op(ytransl_cycles)
ytransl_op = ytransl_op
symm_projs, kxs, kys = symm.get2DTranslationProjectors(
xtransl_op, max_cycle_len_translx, ytransl_op,
max_cycle_len_transly)
eig_vals_sectors = []
for ii, proj in enumerate(symm_projs):
h_sector = spin_model.createH(projector=proj)
eig_vals_sector, eig_vects_sector = spin_model.diagH(h_sector)
eig_vals_sectors.append(eig_vals_sector)
# why only accurate to 10 decimal places?
eigs_all_sectors = np.sort(np.concatenate(eig_vals_sectors))
max_diff = np.abs(eig_vals_full - eigs_all_sectors).max()
self.assertAlmostEqual(max_diff, 0, 10)
def test_d4_symm(self):
"""
Test d4 symmetry by diagonalizing random spin system with and without it
:return:
"""
cluster = geom.Geometry.createSquareGeometry(3,
3,
0,
0,
bc1_open=False,
bc2_open=False)
jx = np.random.rand()
jy = np.random.rand()
jz = np.random.rand()
hx = np.random.rand()
hy = np.random.rand()
hz = np.random.rand()
# diagonalize full hamiltonian
spin_model = tvi.spinSystem(cluster,
jx,
jy,
jz,
hx,
hy,
hz,
use_ryd_detunes=0)
hamiltonian_full = spin_model.createH()
eig_vals_full, eig_vects_full = spin_model.diagH(hamiltonian_full)
# use rotationl symmetry
cx, cy = spin_model.geometry.get_center_of_mass()
rot_fn = symm.getRotFn(4, cx=cx, cy=cy)
rot_cycles, max_cycle_len_rot = symm.findSiteCycles(
rot_fn, spin_model.geometry)
rot_op = spin_model.get_xform_op(rot_cycles)
refl_fn = symm.getReflFn(np.array([0, 1]), cx=cx, cy=cy)
refl_cycles, max_cycle_len_ref = symm.findSiteCycles(
refl_fn, spin_model.geometry)
refl_op = spin_model.get_xform_op(refl_cycles)
symm_projs = symm.getD4Projectors(rot_op, refl_op)
eig_vals_sectors = []
for ii, proj in enumerate(symm_projs):
h_sector = spin_model.createH(projector=proj)
eig_vals_sector, eig_vects_sector = spin_model.diagH(h_sector)
eig_vals_sectors.append(eig_vals_sector)
# why only accurate to 10 decimal places?
eigs_all_sectors = np.sort(np.concatenate(eig_vals_sectors))
max_diff = np.abs(eig_vals_full - eigs_all_sectors).max()
self.assertAlmostEqual(max_diff, 0, 10)
def test_four_by_four_xy_model_symm(self):
"""
Test exact diagonalization of 4x4 xy model with periodic boundary conditions
reference: J. Phys. A: Math. Gen 32 51 (1999).
"Finite-size scaling in the spin-1/2 xy model on a square lattice" by C J Hamer et al
"""
cluster = geom.Geometry.createSquareGeometry(4,
4,
0,
0,
bc1_open=False,
bc2_open=False)
# diagonalize full hamiltonian
spin_model = tvi.spinSystem(cluster,
jx=-1.0,
jy=-1.0,
jz=0.0,
hx=0.0,
hy=0.0,
hz=0.0,
use_ryd_detunes=0)
# x-translations
xtransl_fn = symm.getTranslFn(np.array([[1], [0]]))
xtransl_cycles, max_cycle_len_translx = symm.findSiteCycles(
xtransl_fn, spin_model.geometry)
xtransl_op = spin_model.get_xform_op(xtransl_cycles)
xtransl_op = xtransl_op
# y-translations
ytransl_fn = symm.getTranslFn(np.array([[0], [1]]))
ytransl_cycles, max_cycle_len_transly = symm.findSiteCycles(
ytransl_fn, spin_model.geometry)
ytransl_op = spin_model.get_xform_op(ytransl_cycles)
ytransl_op = ytransl_op
symm_projs, kxs, kys = symm.get2DTranslationProjectors(
xtransl_op, max_cycle_len_translx, ytransl_op,
max_cycle_len_transly)
eig_vals_sectors = []
hfull = spin_model.createH()
for ii, proj in enumerate(symm_projs):
h_sector = proj * hfull * proj.conj().transpose()
eig_vals_sector, eig_vects_sector = spin_model.diagH(
h_sector, print_results=True)
eig_vals_sectors.append(eig_vals_sector)
# why only accurate to 10 decimal places?
eigs_all_sectors = np.sort(np.concatenate(eig_vals_sectors))
min_eig_per_site = eigs_all_sectors[0] / spin_model.geometry.nsites
self.assertAlmostEqual(min_eig_per_site, -1.124972697436, 12)
def test_d2_symmetry_3by3(self):
"""
Test D2 symmetry (generated by 180 degree rotation and a reflection) on a 3x3 Hubbard cluster
with open boundary conditions.
:return:
"""
# todo: do all number sectors
U = 20 * (np.random.rand() - 0.5)
t = np.random.rand()
gm = geom.Geometry.createSquareGeometry(3,
3,
0,
0,
bc1_open=False,
bc2_open=False)
model = ed_fermions.fermions(gm, U, t, ns=np.array([3, 4]), nspecies=2)
# no symmetry
hamiltonian_full = model.createH(projector=model.n_projector)
eig_vals_full, eig_vects_full = model.diagH(hamiltonian_full)
# rotational symmetry
cx, cy = model.geometry.get_center_of_mass()
rot_fn = symm.getRotFn(2, cx=cx, cy=cy)
rot_cycles, max_cycle_len_rot = symm.findSiteCycles(
rot_fn, model.geometry)
rot_op_full = model.get_xform_op(rot_cycles)
rot_op = model.n_projector.dot(
rot_op_full.dot(model.n_projector.conj().transpose()))
# reflection symmetry
refl_fn = symm.getReflFn(np.array([[0], [1]]), cx=cx, cy=cy)
refl_cycles, max_cycle_len_refl = symm.findSiteCycles(
refl_fn, model.geometry)
refl_op_full = model.get_xform_op(refl_cycles)
refl_op = model.n_projector.dot(
refl_op_full.dot(model.n_projector.conj().transpose()))
symm_projs = symm.getD2Projectors(rot_op, refl_op)
eig_vals_sectors = []
for ii, proj in enumerate(symm_projs):
h_sector = model.createH(projector=proj.dot(model.n_projector))
eig_vals_sector, eig_vects_sector = model.diagH(h_sector)
eig_vals_sectors.append(eig_vals_sector)
# why only accurate to 10 decimal places?
eigs_all_sectors = np.sort(np.concatenate(eig_vals_sectors))
max_diff = np.abs(eig_vals_full - eigs_all_sectors).max()
self.assertAlmostEqual(max_diff, 0, 10)
def test_d3_symm_6sites(self):
adjacency_mat = np.array([[0, 1, 0, 1, 0, 0], [1, 0, 1, 1, 1, 0],
[0, 1, 0, 0, 1, 0], [1, 1, 0, 0, 1, 1],
[0, 1, 1, 1, 0, 1], [0, 0, 0, 1, 1, 0]])
cluster = geom.Geometry.createNonPeriodicGeometry(
xlocs=(0, 1, 2, 0.5, 1.5, 1),
ylocs=(0, 0, 0, np.sqrt(3) / 2, np.sqrt(3) / 2, np.sqrt(3)),
adjacency_mat=adjacency_mat)
jx = np.random.rand()
jy = np.random.rand()
jz = np.random.rand()
hx = np.random.rand()
hy = np.random.rand()
hz = np.random.rand()
# diagonalize full hamiltonian
spin_model = tvi.spinSystem(cluster,
jx,
jy,
jz,
hx,
hy,
hz,
use_ryd_detunes=0)
hamiltonian_full = spin_model.createH()
eig_vals_full, eig_vects_full = spin_model.diagH(hamiltonian_full)
# use rotationl symmetry
# triangle center
cx, cy = 1, 1 / np.sqrt(3)
rot_fn = symm.getRotFn(3, cx=cx, cy=cy)
rot_cycles, max_cycle_len_rot = symm.findSiteCycles(
rot_fn, spin_model.geometry)
rot_op = spin_model.get_xform_op(rot_cycles)
refl_fn = symm.getReflFn(np.array([0, 1]), cx=cx, cy=cy)
refl_cycles, max_cycle_len_ref = symm.findSiteCycles(
refl_fn, spin_model.geometry)
refl_op = spin_model.get_xform_op(refl_cycles)
symm_projs = symm.getD3Projectors(rot_op, refl_op)
eig_vals_sectors = []
for ii, proj in enumerate(symm_projs):
h_sector = spin_model.createH(projector=proj)
eig_vals_sector, eig_vects_sector = spin_model.diagH(h_sector)
eig_vals_sectors.append(eig_vals_sector)
eigs_all_sectors = np.sort(np.concatenate(eig_vals_sectors))
max_diff = np.abs(eig_vals_full - eigs_all_sectors).max()
self.assertAlmostEqual(max_diff, 0, 12)
def test_d3_symm_3sites(self):
"""
Test d3 symmetry by diagonalizing random spin system with and without it
:return:
"""
# adjacency_mat = np.array([[0, 1, 1], [1, 0, 1], [1, 1, 0]])
# cluster = geom.Geometry.createNonPeriodicGeometry(xlocs=(0,0.5,1), ylocs=(0,np.sqrt(3)/2,0), adjacency_mat=adjacency_mat)
cluster = geom.Geometry.createRegularPolygonGeometry(3)
jx = np.random.rand()
jy = np.random.rand()
jz = np.random.rand()
hx = np.random.rand()
hy = np.random.rand()
hz = np.random.rand()
# diagonalize full hamiltonian
spin_model = tvi.spinSystem(cluster,
jx,
jy,
jz,
hx,
hy,
hz,
use_ryd_detunes=0)
hamiltonian_full = spin_model.createH()
eig_vals_full, eig_vects_full = spin_model.diagH(hamiltonian_full)
# use rotationl symmetry
rot_fn = symm.getRotFn(3)
rot_cycles, max_cycle_len_rot = symm.findSiteCycles(
rot_fn, spin_model.geometry)
rot_op = spin_model.get_xform_op(rot_cycles)
refl_fn = symm.getReflFn(np.array([0, 1]))
refl_cycles, max_cycle_len_ref = symm.findSiteCycles(
refl_fn, spin_model.geometry)
refl_op = spin_model.get_xform_op(refl_cycles)
symm_projs = symm.getD3Projectors(rot_op, refl_op)
eig_vals_sectors = []
for ii, proj in enumerate(symm_projs):
h_sector = spin_model.createH(projector=proj)
eig_vals_sector, eig_vects_sector = spin_model.diagH(h_sector)
eig_vals_sectors.append(eig_vals_sector)
# why only accurate to 10 decimal places?
eigs_all_sectors = np.sort(np.concatenate(eig_vals_sectors))
max_diff = np.abs(eig_vals_full - eigs_all_sectors).max()
self.assertAlmostEqual(max_diff, 0, 12)
def test_translation_symmetry_3by3(self):
"""
Test translational symmetry for a 3x3 Hubbard system with periodic boundary conditions
:return:
"""
U = 20 * (np.random.rand() - 0.5)
t = np.random.rand()
gm = geom.Geometry.createSquareGeometry(3,
3,
0,
0,
bc1_open=False,
bc2_open=False)
hubbard = ed_fermions.fermions(gm, U, t, ns=np.array([1, 1]))
# no symmetry
hamiltonian_full = hubbard.createH(projector=hubbard.n_projector)
eig_vals_full, eig_vects_full = hubbard.diagH(hamiltonian_full)
# with symmetry
xtransl_fn = symm.getTranslFn(np.array([[1], [0]]))
xtransl_cycles, max_cycle_len_translx = symm.findSiteCycles(
xtransl_fn, hubbard.geometry)
xtransl_op = hubbard.n_projector * hubbard.get_xform_op(
xtransl_cycles) * hubbard.n_projector.conj().transpose()
# y-translations
ytransl_fn = symm.getTranslFn(np.array([[0], [1]]))
ytransl_cycles, max_cycle_len_transly = symm.findSiteCycles(
ytransl_fn, hubbard.geometry)
ytransl_op = hubbard.n_projector * hubbard.get_xform_op(
ytransl_cycles) * hubbard.n_projector.conj().transpose()
symm_projs, kxs, kys = symm.get2DTranslationProjectors(
xtransl_op, max_cycle_len_translx, ytransl_op,
max_cycle_len_transly)
eig_vals_sectors = []
for ii, proj in enumerate(symm_projs):
h_sector = hubbard.createH(projector=proj.dot(hubbard.n_projector))
eig_vals_sector, eig_vects_sector = hubbard.diagH(h_sector)
eig_vals_sectors.append(eig_vals_sector)
# why only accurate to 10 decimal places?
eigs_all_sectors = np.sort(np.concatenate(eig_vals_sectors))
max_diff = np.abs(eig_vals_full - eigs_all_sectors).max()
self.assertAlmostEqual(max_diff, 0, 10)
def test_d7_symm_7sites(self):
cluster = geom.Geometry.createRegularPolygonGeometry(7)
jx = np.random.rand()
jy = np.random.rand()
jz = np.random.rand()
hx = np.random.rand()
hy = np.random.rand()
hz = np.random.rand()
# diagonalize full hamiltonian
spin_model = tvi.spinSystem(cluster,
jx,
jy,
jz,
hx,
hy,
hz,
use_ryd_detunes=0)
hamiltonian_full = spin_model.createH()
eig_vals_full, eig_vects_full = spin_model.diagH(hamiltonian_full)
# use rotationl symmetry
rot_fn = symm.getRotFn(7)
rot_cycles, max_cycle_len_rot = symm.findSiteCycles(
rot_fn, spin_model.geometry)
rot_op = spin_model.get_xform_op(rot_cycles)
refl_fn = symm.getReflFn(np.array([0, 1]))
refl_cycles, max_cycle_len_ref = symm.findSiteCycles(
refl_fn, spin_model.geometry)
refl_op = spin_model.get_xform_op(refl_cycles)
symm_projs = symm.getD6Projectors(rot_op, refl_op)
eig_vals_sectors = []
for ii, proj in enumerate(symm_projs):
h_sector = spin_model.createH(projector=proj)
eig_vals_sector, eig_vects_sector = spin_model.diagH(h_sector)
eig_vals_sectors.append(eig_vals_sector)
eigs_all_sectors = np.sort(np.concatenate(eig_vals_sectors))
max_diff = np.abs(eig_vals_full - eigs_all_sectors).max()
self.assertAlmostEqual(max_diff, 0, 14)
def test_findSiteCycles(self):
"""
Test function which finds cyclese of sites under repeated transformations
:return:
"""
geom = ed_geometry.Geometry.createSquareGeometry(4, 4, 0, 0, 1, 1)
cx, cy = geom.get_center_of_mass()
permutation = geom.get_sorting_permutation('top_alternating')
geom.permute_sites(permutation)
rot_fn = ed_symmetry.getRotFn(4, cx=cx, cy=cy)
cycles, max_cycle_len = ed_symmetry.findSiteCycles(rot_fn, geom)
cycles_expected = [[0, 15, 12, 3], [1, 8, 13, 4], [2, 7, 14, 11], [5, 6, 9, 10]]
self.assertEqual(max_cycle_len, 4)
self.assertEqual(cycles, cycles_expected)
with np.errstate(divide="ignore"):
betas = np.divide(1, temps)
betas[temps == 0] = np.inf
# ints = np.linspace(0, 5, 60) * t
ints = np.linspace(0, 5, 5) * t
ints = np.concatenate((-np.flip(ints, axis=0), ints[1:]))
print("spinless fermions with nearest neighbor interactions")
print("nsites = %d, n interactions = %d, ntemps = %d" % (nsites, len(ints), len(temps)))
gm = geom.Geometry.createSquareGeometry(nsites, 1, 0, 0, bc1_open=False, bc2_open=True)
# translational symmetry
xtransl_fn = symm.getTranslFn(np.array([[1], [0]]))
xtransl_cycles, max_cycle_len_translx = symm.findSiteCycles(xtransl_fn, gm)
# get all symmetry operators at the beginning
n_list = np.array([])
k_list = np.array([])
projector_list = []
sf = ed_fermions.fermions(gm, 0, t, us_same_species=0, potentials=0, nspecies=1)
# number subspace projectors
n_species_op = sf.get_sum_op(sf.n_op, 0, format="boson")
n_projs, ns = sf.get_subspace_projs(n_species_op, print_results=False)
# translation op
xtransl_op_full = sf.get_xform_op(xtransl_cycles)
# get all projectors
import ed_geometry as geom import ed_spins as spins import ed_symmetry as symm # set up system J = 1 gm = geom.Geometry.createSquareGeometry(10, 1, 0, 0, bc1_open=False, bc2_open=True) ss = spins.spinSystem(gm, jx=J, jy=J, jz=J) # total sz and spin flip op sz_op = ss.get_sum_op(ss.sz) sz_flip_op = ss.get_swap_up_down_op() # translation operators xtransl_fn = symm.getTranslFn(np.array([[1], [0]])) xtransl_cycles, ntranslations = symm.findSiteCycles(xtransl_fn, ss.geometry) tx_op = ss.get_xform_op(xtransl_cycles) # inversion op cx, cy = ss.geometry.get_center_of_mass() inv_fn = symm.getInversionFn(cx, cy) inv_cycles, _ = symm.findSiteCycles(inv_fn, ss.geometry) inv_op = ss.get_xform_op(inv_cycles) # get projectors on mz subspace mz_projs, mzs = ss.get_subspace_projs(sz_op.tocsr()) # sequentially get projectors on mz the x-translation (then spin flip for mz=0 sector only) projs = [] mzs_all = [] kxs_all = []
def test_full_symm_3x3(self):
cluster = geom.Geometry.createSquareGeometry(3,
3,
0,
0,
bc1_open=False,
bc2_open=False)
jx = np.random.rand()
jy = np.random.rand()
jz = np.random.rand()
hx = np.random.rand()
hy = np.random.rand()
hz = np.random.rand()
# diagonalize full hamiltonian
spin_model = tvi.spinSystem(cluster,
jx,
jy,
jz,
hx,
hy,
hz,
use_ryd_detunes=0)
hamiltonian_full = spin_model.createH()
eig_vals_full, eig_vects_full = spin_model.diagH(hamiltonian_full)
xtransl_fn = symm.getTranslFn(np.array([[1], [0]]))
xtransl_cycles, max_cycle_len_translx = symm.findSiteCycles(
xtransl_fn, spin_model.geometry)
tx_op = spin_model.get_xform_op(xtransl_cycles)
# y-translations
ytransl_fn = symm.getTranslFn(np.array([[0], [1]]))
ytransl_cycles, max_cycle_len_transly = symm.findSiteCycles(
ytransl_fn, spin_model.geometry)
ty_op = spin_model.get_xform_op(ytransl_cycles)
# rotation
cx, cy = spin_model.geometry.get_center_of_mass()
rot_fn = symm.getRotFn(4, cx=cx, cy=cy)
rot_cycles, max_cycle_len_rot = symm.findSiteCycles(
rot_fn, spin_model.geometry)
rot_op = spin_model.get_xform_op(rot_cycles)
# reflection
# reflection about y-axis
refl_fn = symm.getReflFn(np.array([0, 1]), cx=cx, cy=cy)
refl_cycles, max_cycle_len_refl = symm.findSiteCycles(
refl_fn, spin_model.geometry)
refl_op = spin_model.get_xform_op(refl_cycles)
symm_projs = symm.getC4V_and_3byb3(rot_op, refl_op, tx_op, ty_op)
eig_vals_sectors = []
for ii, proj in enumerate(symm_projs):
h_sector = spin_model.createH(projector=proj)
eig_vals_sector, eig_vects_sector = spin_model.diagH(h_sector)
eig_vals_sectors.append(eig_vals_sector)
# why only accurate to 10 decimal places?
eigs_all_sectors = np.sort(np.concatenate(eig_vals_sectors))
max_diff = np.abs(eig_vals_full - eigs_all_sectors).max()
self.assertAlmostEqual(max_diff, 0, 10)
def test_ising_model_5x5(self):
"""
Test diagonalization of 5x5 ising model with periodic boundary conditions.
reference: J. Phys. A: Math. Gen 33 6683 (2000).
"Finite-size scaling in the transverse Ising model on a square lattice" by C J Hamer
https://doi.org/10.1088/0305-4470/33/38/303
:return:
"""
cluster = geom.Geometry.createSquareGeometry(5,
5,
0,
0,
bc1_open=False,
bc2_open=False)
# paper definition of hamiltonian differs by a factor of two from mine
jz_critical = -2 * 0.32669593806
h_transverse = 2 * 1.0
spin_model = tvi.spinSystem(cluster,
jx=0.0,
jy=0.0,
jz=jz_critical,
hx=h_transverse,
hy=0.0,
hz=0.0,
use_ryd_detunes=0)
# symmetry swapping up/down spins
spin_swap_op = spin_model.get_swap_up_down_op()
# x-translations
xtransl_fn = symm.getTranslFn(np.array([[1], [0]]))
xtransl_cycles, max_cycle_len_translx = symm.findSiteCycles(
xtransl_fn, spin_model.geometry)
xtransl_op = spin_model.get_xform_op(xtransl_cycles)
xtransl_op = xtransl_op
# y-translations
ytransl_fn = symm.getTranslFn(np.array([[0], [1]]))
ytransl_cycles, max_cycle_len_transly = symm.findSiteCycles(
ytransl_fn, spin_model.geometry)
ytransl_op = spin_model.get_xform_op(ytransl_cycles)
ytransl_op = ytransl_op
symm_projs, kxs, kys = symm.get2DTranslationProjectors(
xtransl_op, max_cycle_len_translx, ytransl_op,
max_cycle_len_transly)
eig_vals_sectors = []
full_proj_list = []
hfull = spin_model.createH()
for ii, proj in enumerate(symm_projs):
spin_swap_proj_op = proj * spin_swap_op * proj.conj().transpose()
# char_table = np.array([[1, 1], [1, -1]])
# ccs = [[sp.eye(spin_swap_proj_op.shape[0], format="csr")], [spin_swap_proj_op]]
swap_projs, phase = symm.getZnProjectors(spin_swap_proj_op, 2)
for jj, sproj in enumerate(swap_projs):
full_proj_list.append(sproj * proj)
h_sector = sproj * proj * hfull * proj.conj().transpose(
) * sproj.conj().transpose()
eig_vals_sector, eig_vects_sector = spin_model.diagH(
h_sector, print_results=True)
eig_vals_sectors.append(eig_vals_sector)
# why only accurate to 10 decimal places?
eigs_all_sectors = np.sort(np.concatenate(eig_vals_sectors))
min_eig_per_site = eigs_all_sectors[0] / spin_model.geometry.nsites + 1
self.assertAlmostEqual(min_eig_per_site, -0.064637823298, 11)
bc1_open=False,
bc2_open=False)
parent_geometry.permute_sites(parent_geometry.get_sorting_permutation())
model = tvi.spinSystem(parent_geometry,
jx,
jy,
jz,
hx,
hy,
hz,
use_ryd_detunes=False)
# x-translation
tx_fn = symm.getTranslFn(np.array([[1], [0]]))
tx_cycles, ntx = symm.findSiteCycles(tx_fn, model.geometry)
tx_op = model.get_xform_op(tx_cycles)
# y-translations
ty_fn = symm.getTranslFn(np.array([[0], [1]]))
ty_cycles, nty = symm.findSiteCycles(ty_fn, model.geometry)
ty_op = model.get_xform_op(ty_cycles)
# symmetry projectors
symm_projs, kxs, kys = symm.get2DTranslationProjectors(tx_op,
ntx,
ty_op,
nty,
print_results=True)
# Calculate eigenvalues and expectation values for each symmetry sector
