def test(sps, Lx, Ly):
N = Lx * Ly
nmax = sps - 1
tr = square_lattice_trans(Lx, Ly)
basis_dict = {}
Nbs = range(nmax * N + 1)
for Nb in Nbs:
basis_blocks = []
pcon_basis = boson_basis_general(N, Nb=Nb, sps=sps)
Ns_block = 0
for blocks in tr.allowed_blocks_iter():
basis = boson_basis_general(N, Nb=Nb, sps=sps, **blocks)
Ns_block += basis.Ns
basis_blocks.append(basis)
try:
assert (Ns_block == pcon_basis.Ns)
except AssertionError:
print(Ns_block, pcon_basis.Ns)
raise AssertionError
basis_dict[Nb] = (pcon_basis, basis_blocks)
J = [[1.0, i, tr.T_x[i]] for i in range(N)]
J.extend([[1.0, i, tr.T_y[i]] for i in range(N)])
static = [["nn", J], ["+-", J], ["-+", J]]
E_symm = {}
for Nb, (pcon_basis, basis_blocks) in basis_dict.items():
H_pcon = hamiltonian(static, [], basis=pcon_basis, dtype=np.float64)
if H_pcon.Ns > 0:
E_pcon = np.linalg.eigvalsh(H_pcon.todense())
else:
E_pcon = np.array([])
E_block = []
for basis in basis_blocks:
H = hamiltonian(static, [], basis=basis, dtype=np.complex128)
if H.Ns > 0:
E_block.append(np.linalg.eigvalsh(H.todense()))
E_block = np.hstack(E_block)
E_block.sort()
np.testing.assert_allclose(E_pcon, E_block, atol=1e-13)
print("passed Nb={} sector".format(Nb))
def __init__(self, U, z, max_p, L): #initialises object parameters
self.U = U
self.z = z - 2 #effective z is different to 'number of nearest neighbours' z, depends on positioning
self.L = L
self.basis = boson_basis_general(self.L,
sps=max_p + 1) #basis generation
self.local_z = [self.z for i in range(self.L)] #local_z list
self.local_z[0] = self.local_z[0] + 1
self.local_z[self.L - 1] = self.local_z[
self.L - 1] + 1 #differences in the z for the ends of the chain
U = 1.0 # onsite interaction
mu = 0.371 # chemical potential
#
###### setting up user-defined symmetry transformations for 2d lattice ######
s = np.arange(N_2d) # sites [0,1,2,....]
x = s % Lx # x positions for sites
y = s // Lx # y positions for sites
T_x = (x + 1) % Lx + Lx * y # translation along x-direction
T_y = x + Lx * ((y + 1) % Ly) # translation along y-direction
P_x = x + Lx * (Ly - y - 1) # reflection about x-axis
P_y = (Lx - x - 1) + Lx * y # reflection about y-axis
#
###### setting up bases ######
basis_2d = boson_basis_general(N_2d,
sps=N_sps,
kxblock=(T_x, 0),
kyblock=(T_y, 0),
pxblock=(P_x, 0),
pyblock=(P_y, 0))
#
###### setting up hamiltonian ######
# setting up site-coupling lists
#hopping=[[-J,i,T_x[i]] for i in range(N_2d)] + [[-J,i,T_y[i]] for i in range(N_2d)]
potential = [[-mu - U / 2.0, i] for i in range(N_2d)]
interaction = [[U / 2.0, i, i] for i in range(N_2d)]
#
print("# J E/N")
for J in np.linspace(0, 0.1, 41): # hopping matrix element
hopping = [[-J, i, T_x[i]] for i in range(N_2d)] + [[-J, i, T_y[i]]
for i in range(N_2d)]
static = [["+-", hopping], ["-+", hopping], ["n", potential],
["nn", interaction]]
T_y = x +Lx*((y+1)%Ly) # translation along y-direction R = np.rot90(s.reshape(Lx,Ly), axes=(0,1)).reshape(N_2d) # rotate P_x = x + Lx*(Ly-y-1) # reflection about x-axis P_y = (Lx-x-1) + Lx*y # reflection about y-axis Z = -(s+1) # spin inversion # ###### setting up bases ###### basis_boson = boson_basis_general(N_2d, make_basis=False, Nb=N_2d//4,sps=2, kxblock=(T_x,0),kyblock=(T_y,0), rblock=(R,0), pxblock=(P_x,0),pyblock=(P_y,0), # zblock=(Z,0) ) basis_boson_full = boson_basis_general(N_2d, make_basis=True, Nb=N_2d//4,sps=2, ) basis_spin = spin_basis_general(N_2d, pauli=False, make_basis=False, Nup=N_2d//2, kxblock=(T_x,0),kyblock=(T_y,0), rblock=(R,0), pxblock=(P_x,0),pyblock=(P_y,0), zblock=(Z,0)
J = np.sqrt(7)
J_p = [[+J, i, T_x[i]] for i in range(N_2d)] + [[+J, i, T_y[i]]
for i in range(N_2d)]
J_n = [[-J, i, T_x[i]] for i in range(N_2d)] + [[-J, i, T_y[i]]
for i in range(N_2d)]
lattice_trans = square_lattice_trans(Lx, Ly)
allowed_sectors = lattice_trans.allowed_blocks_iter()
for ii, basis_dict in enumerate(allowed_sectors):
###### setting up bases ######
basis_boson = boson_basis_general(N_2d,
make_basis=False,
Nb=N_2d // 4,
sps=2,
**basis_dict)
basis_boson_full = boson_basis_general(
N_2d,
make_basis=False,
Nb=N_2d // 4,
sps=2,
)
basis_spin = spin_basis_general(N_2d,
pauli=False,
make_basis=False,
Nup=N_2d // 2,
zblock=(Z, 0),
basis_op=spinless_fermion_basis_general(N_2d, make_basis=True,
Nf=Np,
kxblock=(T_x,0),kyblock=(T_y,0),
pxblock=(P_x,0),pyblock=(P_y,0),
)
compare(static_list,basis,basis_op)
print('passed spinless fermios')
basis=boson_basis_general(N_2d, make_basis=False,
Nb=Np, sps=3,
kxblock=(T_x,0),kyblock=(T_y,0),
pxblock=(P_x,0),pyblock=(P_y,0),
)
basis_op=boson_basis_general(N_2d, make_basis=True,
Nb=Np, sps=3,
kxblock=(T_x,0),kyblock=(T_y,0),
pxblock=(P_x,0),pyblock=(P_y,0),
)
compare(static_list,basis,basis_op)
print('passed bosons')
sys.path.insert(0, qspin_path)
from quspin.basis import spin_basis_1d, boson_basis_1d, spinless_fermion_basis_1d, spinful_fermion_basis_1d
from quspin.basis import spin_basis_general, boson_basis_general, spinless_fermion_basis_general, spinful_fermion_basis_general
from itertools import product
import numpy as np
for L in [6, 7]:
# symmetry-free
basis_1 = spin_basis_1d(L=L, Nup=range(0, L, 2))
basis_1g = spin_basis_general(N=L, Nup=range(0, L, 2))
basis_2 = boson_basis_1d(L=L, Nb=range(0, L, 2))
basis_2g = boson_basis_general(N=L, Nb=range(0, L, 2))
basis_3 = spinless_fermion_basis_1d(L=L, Nf=range(0, L, 2))
basis_3g = spinless_fermion_basis_general(N=L, Nf=range(0, L, 2))
basis_4 = spinful_fermion_basis_1d(L=L,
Nf=product(range(0, L, 2),
range(0, L, 2)))
basis_4g = spinful_fermion_basis_general(N=L,
Nf=product(
range(0, L, 2),
range(0, L, 2)))
# symmetry-ful
t = (np.arange(L) + 1) % L