def test_Nup(n,m,S):
nmax = int(eval("2*"+S))
N = n**2 + m**2
# Nups=range(nmax*N+1)
Nups = [2]
a_1 = np.array([0,1])
a_2 = np.array([1,0])
T1,t1,T2,t2,Pr,pr,Tx,Ty = tilted_square_transformations(n,m,a_1,a_2)
Jzz = [[-1.0,i,Tx[i]] for i in range(N)]
Jzz.extend([-1.0,i,Ty[i]] for i in range(N))
hx = [[-1.0,i] for i in range(N)]
fzz = lambda x:1-x
fx = lambda x:x
dynamic=[["zz",Jzz,fzz,()],["+-",Jzz,fx,()],["-+",Jzz,fx,()]]
ss = np.linspace(0,1,11)
for Nup in Nups:
basis_full = spin_basis_general(N,S=S,Nup=Nup)
H_full = hamiltonian([],dynamic,basis=basis_full,dtype=np.float64)
E_full = []
for s in ss:
E_full.append(H_full.eigvalsh(time=s))
E_full = np.vstack(E_full)
E_symm = np.zeros((E_full.shape[0],0),dtype=E_full.dtype)
no_checks = dict(check_symm=False,check_pcon=False,check_herm=False)
for blocks in get_blocks(T1,t1,T2,t2,Pr,pr):
basis = spin_basis_general(N,S=S,Nup=Nup,**blocks)
H = hamiltonian([],dynamic,basis=basis,dtype=np.complex128,**no_checks)
if H.Ns == 0:
continue
block,values = zip(*blocks.items())
Tr,qs = zip(*values)
print(basis.Ns,Nup,list(zip(block,qs)))
for Hd in H._dynamic.values():
dH=(Hd-Hd.T.conj())
n = "{} {} {}".format(basis.Ns,Nup,list(zip(block,qs)))
np.testing.assert_allclose(dH.data,0,atol=1e-7,err_msg=str(n))
E_list = []
for i,s in enumerate(ss):
E = H.eigvalsh(time=s)
E_list.append(E)
E_list = np.vstack(E_list)
E_symm = np.hstack((E_symm,E_list))
E_symm.sort(axis=1)
np.testing.assert_allclose(E_symm,E_full,atol=1e-13)
def get_operators(size, Nb):
n, m = size
if Nb % 2 == 1:
S = "{}/2".format(Nb)
else:
S = "{}".format(Nb // 2)
bath_basis = spin_basis_general(1, S=S)
N = n**2 + m**2
Ns_block_est = max((2**N) / (N), 1000)
if n != 0:
T1, t1, T2, t2, Pr, pr, Tx, Ty = tilted_square_transformations(n, m)
blocks = dict(tx=(Tx, 0), ty=(Ty, 0), pb=(Pr, 0))
spin_basis = spin_basis_general(N,
S="1/2",
pauli=True,
Ns_block_est=Ns_block_est,
**blocks)
else:
L = m
tr = square_lattice_trans(L, L)
Tx = tr.T_x
Ty = tr.T_y
blocks = dict(tx=(Tx, 0),
ty=(Ty, 0),
px=(tr.P_x, 0),
py=(tr.P_y, 0),
pd=(tr.P_d, 0))
spin_basis = spin_basis_general(N,
S="1/2",
pauli=True,
Ns_block_est=Ns_block_est,
**blocks)
basis = tensor_basis(spin_basis, bath_basis)
J_list = [[-1.0, i, Tx[i]] for i in range(N)]
J_list.extend([-1.0, i, Ty[i]] for i in range(N))
M_list = [[1.0 / N**2, i, i] for i in range(N)]
M_list += [[2.0 / N**2, i, j] for i in range(N) for j in range(N) if i > j]
kwargs = dict(basis=basis,
dtype=np.float64,
check_symm=False,
check_pcon=False,
check_herm=False)
print size
H_S = hamiltonian([["zz|", J_list]], [], **kwargs)
M2 = hamiltonian([["zz|", M_list]], [], **kwargs)
return H_S, M2
def test(S,Lx,Ly):
N = Lx*Ly
nmax = int(eval("2*"+S))
sps = nmax+1
tr = square_lattice_trans(Lx,Ly)
basis_dict = {}
Nups=range(nmax*N+1)
for Nup in Nups:
basis_blocks=[]
pcon_basis = spin_basis_general(N,Nup=Nup,S=S)
Ns_block = 0
for blocks in tr.allowed_blocks_spin_inversion_iter(Nup,sps):
basis = spin_basis_general(N,Nup=Nup,S=S,**blocks)
Ns_block += basis.Ns
basis_blocks.append(basis)
try:
assert(Ns_block == pcon_basis.Ns)
except AssertionError:
print(Nup,Ns_block,pcon_basis.Ns)
raise AssertionError("reduced blocks don't sum to particle sector.")
basis_dict[Nup] = (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 = [["zz",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 auto_correlator_symm(L, times, S="1/2"):
# define momentum p sector of the GS of the Heisenberg Hamiltonian
if (L // 2) % 2:
p = L // 2 # corresponds to momentum pi
dtype = np.complex128
else:
p = 0
dtype = np.float64
#
# define translation operator
T = (np.arange(L) + 1) % L
# compute the basis in the momentum sector of the GS of the Heisenberg model
basis_p = spin_basis_general(L, S=S, m=0, kblock=(T, p), pauli=False)
# define Heisenberg Hamiltonian
no_checks = dict(check_symm=False, check_herm=False, check_pcon=False)
H = hamiltonian(static, [], basis=basis_p, dtype=dtype, **no_checks)
# compute GS
E, V = H.eigsh(k=1, which="SA")
psi_GS = V[:, 0]
# evolve GS under symmetry-reduced H (gives a trivial phase factor)
psi_GS_t = H.evolve(psi_GS, 0, times)
#
##### compute autocorrelation function foe every momentum sector
Cq_t = np.zeros((times.shape[0], L), dtype=np.complex128)
#
for q in range(L): # sum over symmetry sectors
#
###### define operator O_q, sum over lattice sites
op_list = [[
"z", [j],
(np.sqrt(2.0) / L) * np.exp(-1j * 2.0 * np.pi * q * j / L)
] for j in range(L)]
# compute basis in the (q+p)-momentum sector (the total momentum of O_q|psi_GS> is q+p)
basis_q = spin_basis_general(L,
S=S,
m=0,
kblock=(T, p + q),
pauli=False)
# define Hamiltonian in the q-momentum sector
Hq = hamiltonian(static, [],
basis=basis_q,
dtype=np.complex128,
**no_checks)
# use Op_shift_sector apply operator O_q to GS; the momentum of the new state is p+q
Opsi_GS = basis_q.Op_shift_sector(basis_p, op_list, psi_GS)
# time evolve Opsi_GS under H_q
Opsi_GS_t = Hq.evolve(Opsi_GS, 0.0, times)
# apply operator O on time-evolved psi_t
O_psi_GS_t = basis_q.Op_shift_sector(basis_p, op_list, psi_GS_t)
# compute autocorrelator for every momentum sector
Cq_t[..., q] = np.einsum("ij,ij->j", O_psi_GS_t.conj(), Opsi_GS_t)
#
return np.sum(Cq_t, axis=1) # sum over momentum sectors
def corr_symm(L, times, S="1/2"):
J_list = [[1.0, i, (i + 1) % L] for i in range(L)]
static = [[op, J_list] for op in ["-+", "+-", "zz"]]
if (L // 2) % 2:
q0 = L // 2
dtype = np.complex128
else:
q0 = 0
dtype = np.float64
t = (np.arange(L) + 1) % L
basis = spin_basis_general(L, S=S, m=0, kblock=(t, q0), pauli=False)
kwargs = dict(basis=basis,
dtype=dtype,
check_symm=False,
check_herm=False,
check_pcon=False)
H = hamiltonian(static, [], **kwargs)
E, V = H.eigsh(k=1, which="SA")
psi0 = V[:, 0]
sqs = []
psi0_t = H.evolve(psi0.ravel(), 0, times)
for q in range(L):
op_pq = [["z", [i], (2.0 / L) * np.exp(-2j * np.pi * q * i / L)]
for i in range(L)]
basis_q = spin_basis_general(L,
S=S,
m=0,
kblock=(t, q0 + q),
pauli=False)
kwargs = dict(basis=basis_q,
dtype=np.complex128,
check_symm=False,
check_herm=False,
check_pcon=False)
Hq = hamiltonian(static, [], **kwargs)
psi1 = basis_q.Op_shift_sector(basis, op_pq, psi0)
psi1_t = Hq.evolve(psi1, 0, times)
psi2_t = basis_q.Op_shift_sector(basis, op_pq, psi0_t)
sqs.append(np.einsum("ij,ij->j", psi2_t.conj(), psi1_t))
return sum(sqs)
def get_H(L, pblock=None, zblock=None):
p = np.arange(L)[::-1]
z = -(np.arange(L) + 1)
blocks = {}
if pblock is not None:
blocks["pblock"] = (p, pblock)
if zblock is not None:
blocks["zblock"] = (z, zblock)
basis = spin_basis_general(L, m=0, pauli=False, **blocks)
Jzz_list = [[1.0, i, (i + 1) % L] for i in range(L)]
Jxy_list = [[0.5, i, (i + 1) % L] for i in range(L)]
static = [[op, Jxy_list] for op in ["+-", "-+"]] + [["zz", Jzz_list]]
kwargs = dict(basis=basis,
dtype=np.float64,
check_symm=False,
check_herm=False,
check_pcon=False)
H_LO = quantum_LinearOperator(static, **kwargs)
H = hamiltonian(static, [], **kwargs)
return H_LO, H
def corr_nosymm(L, times, S="1/2"):
J_list = [[1.0, i, (i + 1) % L] for i in range(L)]
static = [[op, J_list] for op in ["-+", "+-", "zz"]]
basis = spin_basis_general(L, S=S, m=0, pauli=False)
kwargs = dict(basis=basis,
dtype=np.float64,
check_symm=False,
check_herm=False,
check_pcon=False)
H = hamiltonian(static, [], **kwargs)
E, V = H.eigsh(k=1, which="SA")
psi0 = V[:, 0]
psi0_t = H.evolve(psi0, 0, times)
sqs = []
op_list = [["z", [0], 2.0]]
# import inspect
# print(inspect.getsource(basis.inplace_Op))
psi1 = basis.inplace_Op(psi0, op_list, np.float64)
psi1_t = H.evolve(psi1, 0, times)
psi2_t = basis.inplace_Op(psi0_t, op_list, np.float64)
sqs.append(np.einsum("ij,ij->j", psi2_t.conj(), psi1_t))
return sum(sqs)
def auto_correlator(L, times, S="1/2"):
# construct basis in zero magnetization sector: no lattice symmetries
basis = spin_basis_general(L, S=S, m=0, pauli=False)
# define Heisenberg Hamiltonian
no_checks = dict(check_symm=False, check_herm=False, check_pcon=False)
H = hamiltonian(static, [], basis=basis, dtype=np.float64, **no_checks)
# compute GS
E, V = H.eigsh(k=1, which="SA")
psi_GS = V[:, 0]
# evolve GS under H (gives a trivial phase factor)
psi_GS_t = H.evolve(psi_GS, 0.0, times)
#
###### define operator O to compute the autocorrelation function of
#
op_list = [["z", [0], np.sqrt(2.0)]]
# use inplace_Op to apply operator O on psi_GS
Opsi_GS = basis.inplace_Op(psi_GS, op_list, np.float64)
# time evolve Opsi_GS under H
Opsi_GS_t = H.evolve(Opsi_GS, 0.0, times)
# apply operator O on time-evolved psi_t
O_psi_GS_t = basis.inplace_Op(psi_GS_t, op_list, np.float64)
# compute autocorrelator
C_t = np.einsum("ij,ij->j", O_psi_GS_t.conj(), Opsi_GS_t)
#
return C_t
def make_basis(N_half):
""" Generates a list of integers to represent external, user-imported basis """
old_basis = spin_basis_general(N_half, m=0)
#
states = old_basis.states
shift_states = np.left_shift(states, N_half)
#
shape = states.shape + states.shape
#
states_b = np.broadcast_to(states, shape)
shift_states_b = np.broadcast_to(shift_states, shape)
# this does the kronecker sum in a more memory efficient way.
return (states_b + shift_states_b.T).ravel()
def exact_diag(J,Hx,Hz,Lx,Ly):
N_2d = Lx*Ly # number of sites
###### 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
mT_y = x +Lx*((y+Ly-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
Z = -(s+1) # spin inversion
###### setting up bases ######
# basis_2d = spin_basis_general(N=N_2d,S="1/2",pauli=0)
basis_2d = spin_basis_general(N=N_2d,S="1/2",pauli=0,kxblock=(T_x,0),kyblock=(T_y,0))
###### setting up hamiltonian ######
# setting up site-coupling lists
Jzzs = [[J,i,T_x[i]] for i in range(N_2d)]+[[J,i,T_y[i]] for i in range(N_2d)]
Hxs = [[-Hx,i] for i in range(N_2d)]
Hzs = [[-Hz,i] for i in range(N_2d)]
static = [["zz",Jzzs],["x",Hxs],["z",Hzs]]
# build hamiltonian
# H = hamiltonian(static,[],static_fmt="csr",basis=basis_2d,dtype=np.float64)
no_checks = dict(check_symm=False, check_pcon=False, check_herm=False)
H = hamiltonian(static,[],static_fmt="csr",basis=basis_2d,dtype=np.float64,**no_checks)
# diagonalise H
ene,vec = H.eigsh(time=0.0,which="SA",k=2)
# ene = H.eigsh(time=0.0,which="SA",k=2,return_eigenvectors=False); ene = np.sort(ene)
norm2 = np.linalg.norm(vec[:,0])**2
# calculate uniform magnetization
int_mx = [[1.0,i] for i in range(N_2d)]
int_mz = [[1.0,i] for i in range(N_2d)]
static_mx = [["x",int_mx]]
static_mz = [["z",int_mz]]
op_mx = hamiltonian(static_mx,[],static_fmt="csr",basis=basis_2d,dtype=np.float64,**no_checks).tocsr(time=0)
op_mz = hamiltonian(static_mz,[],static_fmt="csr",basis=basis_2d,dtype=np.float64,**no_checks).tocsr(time=0)
mx = (np.conjugate(vec[:,0]).dot(op_mx.dot(vec[:,0])) / norm2).real / N_2d
mz = (np.conjugate(vec[:,0]).dot(op_mz.dot(vec[:,0])) / norm2).real / N_2d
# calculate n.n. sz.sz correlation
int_mz0mz1 = [[1.0,i,T_x[i]] for i in range(N_2d)]+[[1.0,i,T_y[i]] for i in range(N_2d)]
static_mz0mz1 = [["zz",int_mz0mz1]]
op_mz0mz1 = hamiltonian(static_mz0mz1,[],static_fmt="csr",basis=basis_2d,dtype=np.float64,**no_checks).tocsr(time=0)
mz0mz1 = (np.conjugate(vec[:,0]).dot(op_mz0mz1.dot(vec[:,0])) / norm2).real / N_2d
# calculate sz(0,0).sz(1,1) correlation
int_mz0mzsq2 = [[1.0,i,T_y[T_x[i]]] for i in range(N_2d)]+[[1.0,i,mT_y[T_x[i]]] for i in range(N_2d)]
static_mz0mzsq2 = [["zz",int_mz0mzsq2]]
op_mz0mzsq2 = hamiltonian(static_mz0mzsq2,[],static_fmt="csr",basis=basis_2d,dtype=np.float64,**no_checks).tocsr(time=0)
mz0mzsq2 = (np.conjugate(vec[:,0]).dot(op_mz0mzsq2.dot(vec[:,0])) / norm2).real / N_2d
return ene, mx, mz, mz0mz1, mz0mzsq2
def run_computation():
#
###### define model parameters ######
J1=1.0 # spin=spin interaction
J2=0.5 # magnetic field strength
Omega=8.0 # drive frequency
Lx, Ly = 4, 4 # linear dimension of spin 1 2d lattice
N_2d = Lx*Ly # number of sites for spin 1
#
###### setting up user-defined symmetry transformations for 2d lattice ######
sites = np.arange(N_2d) # sites [0,1,2,....]
x = sites%Lx # x positions for sites
y = sites//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
#
T_a = (x+1)%Lx + Lx*((y+1)%Ly) # translation along anti-diagonal
T_d = (x-1)%Lx + Lx*((y+1)%Ly) # translation along diagonal
#
###### setting up bases ######
basis_2d = spin_basis_general(N_2d,pauli=False) # making the basis sped up by OpenMP
print('finished computing basis')
#
###### setting up hamiltonian ######
# set up time-dependence
def drive(t,Omega):
return np.cos(Omega*t)
drive_args=[Omega,]
# setting up site-coupling lists
J1_list=[[J1,i,T_x[i]] for i in range(N_2d)] + [[J1,i,T_y[i]] for i in range(N_2d)]
J2_list=[[J2,i,T_d[i]] for i in range(N_2d)] + [[J2,i,T_a[i]] for i in range(N_2d)]
#
static =[ ["xx",J1_list],["yy",J1_list],["zz",J1_list] ]
dynamic=[ ["xx",J2_list,drive,drive_args],["yy",J2_list,drive,drive_args],["zz",J2_list,drive,drive_args] ]
# build hamiltonian
H=hamiltonian(static,[],basis=basis_2d,dtype=np.float64,check_symm=False,check_herm=False)
# diagonalise H
E,V=H.eigsh(time=0.0,k=50,which='LA') # H.eigsh sped up by MKL
print('finished computing energies')
psi_0=V[:,0]
# evolve state
t=np.linspace(0.0,20*2*np.pi/Omega,21)
psi_t=H.evolve(psi_0,t[0],t,iterate=True) # H.evolve sped up by OpenMP
for j,psi in enumerate(psi_t):
E_t = H.expt_value(psi,time=t[j])
print("finished evolving up to time step {:d}".format(j) )
def maxcut_to_quantum(structure, system_size, fill, interaction_shape,
interaction_radius):
prob = maxcut.initialize_problem(structure, system_size, fill,
interaction_shape, interaction_radius)
N = prob.get_num_vertices()
basis = spin_basis_general(N)
# Hamiltonian terms for Ising interactions and reference field
J_zz = prob.get_edges()
h_x = [[-1, i] for i in range(N)]
# Hamiltonian for Ising interactions
static = [["zz", J_zz]]
dynamic = []
H = hamiltonian(static, dynamic, basis=basis, dtype=np.float64)
# reference Hamiltonian
B = hamiltonian([["x", h_x]], [],
dtype=np.float64,
basis=basis,
check_herm=False,
check_symm=False)
# initial state: all up in x basis (ground state of reference Hamiltonian)
psi_0 = (1 / (2**(N / 2))) * np.ones(2**N, ) # all up in x basis
# exact ground states
states = util.get_states_str(system_size)
ground_state_energy, num_ground_states, ground_states = classical_algorithms.BruteForce(
).solve(prob, allGroundStates=True)
ground_states_id = []
for ground_state in ground_states:
ground_state_str = ''
for v in range(N):
ground_state_str += str(int((ground_state[v] + 1) / 2))
ground_states_id.append(states.index(ground_state_str))
return H, B, psi_0, ground_states_id
def get_operators(L):
N = 2 * L
Tx = (np.arange(L) + 1) % L
Tx = np.hstack((Tx, Tx + L))
P = np.arange(L)[::-1]
P = np.hstack((P, P + L))
basis = spin_basis_general(N, pauli=True, pblk=(P, 0), kblk=(Tx, 0))
J_list = [[-1, i, (i + 1) % L] for i in range(L)]
M_list = [[1.0 / L**2, i, j] for i in range(L) for j in range(L)]
kwargs = dict(basis=basis,
dtype=np.float64,
check_symm=False,
check_pcon=False,
check_herm=False)
print basis.N
H_S = hamiltonian([["zz", J_list]], [], **kwargs)
M2 = hamiltonian([["zz", M_list]], [], **kwargs)
return H_S, M2
err_msg=err_msg)
np.testing.assert_allclose(P.H.dot(v_full),
basis.project_to(v_full, sparse=False),
atol=1e-10,
err_msg=err_msg)
L = 12
assert (L >= 3)
z = -(np.arange(L) + 1)
p = np.arange(L)[::-1]
t = (np.arange(L) + 1) % L
bases = [
spin_basis_general(L),
spin_basis_general(L, Nup=L // 2),
spin_basis_general(L, zb=(z, 0)),
spin_basis_general(L, zb=(z, 1)),
spin_basis_general(L, pb=(p, 0)),
spin_basis_general(L, pb=(p, 1)),
spin_basis_general(L, zb=(z, 0), pb=(p, 0)),
spin_basis_general(L, zb=(z, 0), pb=(p, 1)),
spin_basis_general(L, zb=(z, 1), pb=(p, 0)),
spin_basis_general(L, zb=(z, 1), pb=(p, 1)),
spin_basis_general(L, zb=(z, 0), pb=(t, 0)),
spin_basis_general(L, zb=(z, 0), pb=(t, 1)),
spin_basis_general(L, zb=(z, 1), pb=(t, 0)),
spin_basis_general(L, zb=(z, 1), pb=(t, 1)),
spin_basis_general(L, zb=(z, 0), pb=(p, 0), tb=(t, 0)),
spin_basis_general(L, zb=(z, 0), pb=(p, 0), tb=(t, L - 1)),
def prepare_H_vec(J, Hx, Hz, Lx, Ly):
N_2d = Lx * Ly # number of sites
###### 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
mT_y = x + Lx * ((y + Ly - 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
Z = -(s + 1) # spin inversion
###### setting up bases ######
# basis_2d = spin_basis_general(N=N_2d,S="1/2",pauli=0)
basis_2d = spin_basis_general(N=N_2d,
S="1/2",
pauli=0,
kxblock=(T_x, 0),
kyblock=(T_y, 0))
# print(basis_2d)
# print(basis_2d.Ns)
###### prepare initial state (all down, fock state |000...000> in QuSpin) ######
## http://weinbe58.github.io/QuSpin/generated/quspin.basis.spinful_fermion_basis_1d.html?highlight=partial%20trace#quspin.basis.spinful_fermion_basis_1d.index
## http://weinbe58.github.io/QuSpin/generated/quspin.basis.spin_basis_1d.html#quspin.basis.spin_basis_1d.index
## i0 = basis_2d.index("1111111111111111") # up
# i0 = basis_2d.index("0000000000000000") # down
s_down = "".join("0" for i in range(N_2d))
i_down = basis_2d.index(s_down)
vec = np.zeros(basis_2d.Ns, dtype=np.float64)
vec[i_down] = 1.0
# print(s_down)
# print(i_down)
# print(vec)
###### setting up hamiltonian ######
# setting up site-coupling lists
Jzzs = [[J, i, T_x[i]] for i in range(N_2d)] + [[J, i, T_y[i]]
for i in range(N_2d)]
Hxs = [[-Hx, i] for i in range(N_2d)]
Hzs = [[-Hz, i] for i in range(N_2d)]
static = [["zz", Jzzs], ["x", Hxs], ["z", Hzs]]
# build hamiltonian
# H = hamiltonian(static,[],static_fmt="csr",basis=basis_2d,dtype=np.float64)
no_checks = dict(check_symm=False, check_pcon=False, check_herm=False)
H = hamiltonian(static, [],
static_fmt="csr",
basis=basis_2d,
dtype=np.float64,
**no_checks)
H = H.tocsr(time=0)
# operator for uniform magnetization
int_mx = [[1.0, i] for i in range(N_2d)]
int_mz = [[1.0, i] for i in range(N_2d)]
static_mx = [["x", int_mx]]
static_mz = [["z", int_mz]]
op_mx = hamiltonian(static_mx, [],
static_fmt="csr",
basis=basis_2d,
dtype=np.float64,
**no_checks).tocsr(time=0)
op_mz = hamiltonian(static_mz, [],
static_fmt="csr",
basis=basis_2d,
dtype=np.float64,
**no_checks).tocsr(time=0)
# operator for n.n. sz.sz correlation
int_mz0mz1 = [[1.0, i, T_x[i]]
for i in range(N_2d)] + [[1.0, i, T_y[i]]
for i in range(N_2d)]
static_mz0mz1 = [["zz", int_mz0mz1]]
op_mz0mz1 = hamiltonian(static_mz0mz1, [],
static_fmt="csr",
basis=basis_2d,
dtype=np.float64,
**no_checks).tocsr(time=0)
# operator for sz(0,0).sz(1,1) correlation
int_mz0mzsq2 = [[1.0, i, T_y[T_x[i]]]
for i in range(N_2d)] + [[1.0, i, mT_y[T_x[i]]]
for i in range(N_2d)]
static_mz0mzsq2 = [["zz", int_mz0mzsq2]]
op_mz0mzsq2 = hamiltonian(static_mz0mzsq2, [],
static_fmt="csr",
basis=basis_2d,
dtype=np.float64,
**no_checks).tocsr(time=0)
# operator for sz(0,0).sz(0,2) correlation
int_mz0mz2 = [[1.0, i, T_x[T_x[i]]]
for i in range(N_2d)] + [[1.0, i, T_y[T_y[i]]]
for i in range(N_2d)]
static_mz0mz2 = [["zz", int_mz0mz2]]
op_mz0mz2 = hamiltonian(static_mz0mz2, [],
static_fmt="csr",
basis=basis_2d,
dtype=np.float64,
**no_checks).tocsr(time=0)
return N_2d, H, vec, op_mx, op_mz, op_mz0mz1, op_mz0mzsq2, op_mz0mz2
def compare(static_list,basis,basis_op):
for opstr,indx,J in static_list:
ME,bra,ket = basis.Op_bra_ket(opstr,indx,J,np.float64,basis_op.states)
ME_op,row,col = basis_op.Op(opstr,indx,J,np.float64)
np.testing.assert_allclose(bra - basis_op[row],0.0,atol=1E-5,err_msg='failed bra/row in Op_bra_cket test!')
np.testing.assert_allclose(ket - basis_op[col],0.0,atol=1E-5,err_msg='failed ket/col in Op_bra_ket test!')
np.testing.assert_allclose(ME - ME_op,0.0,atol=1E-5,err_msg='failed ME in Op_bra_ket test!')
for Np in [ None, 2, N_2d-1, [N_2d//4,N_2d//8] ]:
basis=spin_basis_general(N_2d, make_basis=False,
Nup=Np,
kxblock=(T_x,0),kyblock=(T_y,0),
pxblock=(P_x,0),pyblock=(P_y,0),
zblock=(Z,0)
)
basis_op=spin_basis_general(N_2d, make_basis=True,
Nup=Np,
kxblock=(T_x,0),kyblock=(T_y,0),
pxblock=(P_x,0),pyblock=(P_y,0),
zblock=(Z,0)
)
compare(static_list,basis,basis_op)
print('passed spins')
for k in range(L):
for q in range(L):
print("testing k={} -> k+q={}".format(k,(k+q)%L))
# use standard static list for this.
# use generators to generate coupling list
op_list = [["z",[i],np.exp(-2j*np.pi*q*i/L)] for i in range(L)]
#coupling=[[np.exp(-2j*np.pi*q*i/L),i] for i in range(L)]
#op_list = [["z",coupling]]
t = (np.arange(L)+1)%L
b = spin_basis_general(L)
b1 = spin_basis_general(L,kblock=(t,k))
b2 = spin_basis_general(L,kblock=(t,k+q))
# print(b1)
# print(b2)
P1 = b1.get_proj(np.complex128)
P2 = b2.get_proj(np.complex128)
v_in = np.random.normal(0,1,size=b1.Ns) + 1j*np.random.normal(0,1,size=b1.Ns)
v_in /= np.linalg.norm(v_in)
v_in_full = P1.dot(v_in)
v_out_full = b.inplace_Op(v_in_full,op_list,np.complex128)
###### 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
Z = -(s + 1) # spin inversion
#
###### setting up bases ######
basis_2d = spin_basis_general(N=N_2d,
Nup=N_2d // 2,
S="1/2",
pauli=0,
kxblock=(T_x, 0),
kyblock=(T_y, 0),
pxblock=(P_x, 0),
pyblock=(P_y, 0),
zblock=(Z, 0))
#basis_2d = spin_basis_general(N=N_2d,Nup=N_2d//2,S="1/2",pauli=0)
#
###### setting up hamiltonian ######
# setting up site-coupling lists
Jzzs = [[J, i, T_x[i]] for i in range(N_2d)] + [[J, i, T_y[i]]
for i in range(N_2d)]
Jpms = [[0.5 * J, i, T_x[i]] for i in range(N_2d)] + [[0.5 * J, i, T_y[i]]
for i in range(N_2d)]
Jmps = [[0.5 * J, i, T_x[i]] for i in range(N_2d)] + [[0.5 * J, i, T_y[i]]
for i in range(N_2d)]
#
def anneal_bath(L, T, gamma=0.01, path="."):
ti = time.time()
filename = os.path.join(
path, "spin_bath_exact_L_{}_T_{}_gamma_{}.npz".format(L, T, gamma))
if os.path.isfile(filename):
print "file_exists...exiting run."
exit()
N = 2 * L
Tx = (np.arange(L) + 1) % L
Tx = np.hstack((Tx, Tx + L))
P = np.arange(L)[::-1]
P = np.hstack((P, P + L))
print "creating basis"
basis = spin_basis_general(N, pblk=(P, 0), kblk=(Tx, 0))
print "L={}, H-space size: {}".format(L, basis.Ns)
Jzz_list = [[-1, i, (i + 1) % L] for i in range(L)]
hx_list = [[-1, i] for i in range(L)]
hop_bath_list = [[-1.0, L + i, L + (i + 1) % L] for i in range(L)]
hop_bath_list += [[-1.0, L + i, L + (i + 1) % L] for i in range(L)]
int_2_list = [[1.0, L + i, L + (i + 1) % L] for i in range(L)]
int_2_list += [[1.0, L + i, L + (i + 2) % L] for i in range(L)]
int_1_list = [[2.0, L + i] for i in range(L)]
bath_sys_list = [[gamma, i, i + L] for i in range(L)]
Jb_list = [[gamma, i, L + i] for i in range(L)]
A = lambda t: (t / T)**2
B = lambda t: (1 - t / T)**2
static = [["+-", hop_bath_list], ["-+", hop_bath_list], ["zz", int_2_list],
["z", int_1_list]]
dynamic = [
["zz", Jzz_list, A, ()],
["x", hx_list, B, ()],
["+-", bath_sys_list, B, ()],
["-+", bath_sys_list, B, ()],
]
kwargs = dict(basis=basis,
dtype=np.float64,
check_symm=False,
check_pcon=False,
check_herm=False)
H = hamiltonian(static, dynamic, **kwargs)
print "creating hamiltonian"
kwargs = dict(basis=basis,
dtype=np.float64,
check_symm=False,
check_pcon=False,
check_herm=False)
H = hamiltonian([], dynamic, **kwargs)
print "solving initial state"
E0, psi_0 = H.eigsh(k=1, which="SA", time=0)
psi_0 = psi_0.ravel()
print "evolving"
out = np.zeros(psi_0.shape, dtype=np.complex128)
psi_f = evolve(psi_0,
0,
T,
H._hamiltonian__omp_SO,
f_params=(out, ),
solver_name="dop853",
atol=1.1e-15,
rtol=1.1e-15)
psi_f /= np.linalg.norm(psi_f)
print "saving"
np.savez_compressed(filename, psi=psi_f)
print "dome.... {} sec".format(time.time() - ti)
for i in range(N_2d)]
# setting up opstr list
static = [["xx", J1_list], ["yy", J1_list], ["zz", J1_list], ["xx", J2_list],
["yy", J2_list], ["zz", J2_list]]
# convert static list to format which is easy to use with the basis_general.Op and basis_general.Op_bra_ket methods.
static_formatted = _consolidate_static(static)
#
###### setting up basis object without computing the basis (make=False) ######
basis = spin_basis_general(
N_2d,
pauli=0,
make_basis=False,
Nup=N_2d // 2,
kxblock=(T_x, 0),
kyblock=(T_y, 0),
pxblock=(P_x, 0),
pyblock=(P_y, 0),
pdblock=(P_d, 0),
zblock=(Z, 0),
block_order=[
'zblock', 'pdblock', 'pyblock', 'pxblock', 'kyblock', 'kxblock'
] # momentum symmetry comes last for speed
)
print(
basis
) # examine basis: contains a single element because it is not calculated due to make_basis=False argument above.
print('basis is empty [note argument make_basis=False]')
#
###### define quantum state to compute the energy of using Monte-Carlo sampling ######
#
# auxiliary basis, only needed for probability_amplitude(); not needed in a proper variational ansatz.
N_2d = Lx * Ly # number of sites for spin 1
#
###### 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
Z = -(s + 1) # spin inversion
#
###### setting up bases ######
basis_2d = spin_basis_general(N_2d,
kxblock=(T_x, 0),
kyblock=(T_y, 0),
pxblock=(P_x, 0),
pyblock=(P_y, 0),
zblock=(Z, 0))
#
###### setting up hamiltonian ######
# setting up site-coupling lists
Jzz = [[J, i, T_x[i]] for i in range(N_2d)] + [[-1.0, i, T_y[i]]
for i in range(N_2d)]
gx = [[g, i] for i in range(N_2d)]
#
static = [["zz", Jzz], ["x", gx]]
# build hamiltonian
H = hamiltonian(static, [], basis=basis_2d, dtype=np.float64)
# diagonalise H
E = H.eigvalsh()
def makeBasis(N, S1, S2):
basis1 = spin_basis_general(N=N, S=S1)
basis2 = spin_basis_general(N=N, S=S2)
basis = tensor_basis(basis1, basis2)
return basis
import numpy as np
import tempfile, os
def Jr(r, alpha):
return (-1)**(r + 1) / r**(alpha)
L = 10
alpha = 2.0
t = (np.arange(L) + 1) % L
p = np.arange(L)[::-1]
z = -(np.arange(L) + 1)
basis = spin_basis_general(L, m=0.0, t=(t, 0), p=(p, 0), z=(z, 0), pauli=False)
Jzz_list = [[Jr(r, alpha), i, (i + r) % L] for i in range(L)
for r in range(1, L // 2, 1)]
Jxy_list = [[Jr(r, alpha) / 2.0, i, (i + r) % L] for i in range(L)
for r in range(1, L // 2, 1)]
ops = dict(Jxy=[[op, Jxy_list] for op in ["+-", "-+"]],
Jzz=[["zz", Jzz_list]],
Jd=[np.random.normal(0, 1, size=(basis.Ns, basis.Ns))])
op = quantum_operator(ops,
basis=basis,
dtype=np.float32,
matrix_formats=dict(Jzz="dia", Jxy="csr", Jd="dense"))
with tempfile.TemporaryDirectory() as tmpdirname:
L = 34 # or 36 with 10 OMP.MKL threads
output_str = []
######## BASIS CONSTRUCTION ########
#
# required time scales exponentially with L
p = np.arange(L)[::-1]
t = (np.arange(L) + 1) % L
z = -(np.arange(L) + 1)
ti = time.time()
basis = spin_basis_general(L,
S="1/2",
m=0,
kblock=(t, 0),
pblock=(p, 0),
zblock=(z, 0))
tf = time.time()
time_basis = tf - ti
basis_str = "\nbasis with {0:d} states took {1:0.2f} secs.\n".format(
basis.Ns, time_basis)
output_str.append(basis_str)
print(basis_str)
######## HAMILTONIAN CONSTRUCTION ########
#
# required time scales exponentially with L
# linear speedup is expected from both OMP and MKL
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_dict)
basis_spin_full = spin_basis_general(
N_2d,
pauli=False,
make_basis=False,
Nup=N_2d // 2,
)
basis_fermion = spinless_fermion_basis_general(N_2d,
make_basis=False,
Nf=N_2d // 2,
**basis_dict)
def test(Lx,Ly):
N = Lx*Ly
nmax = int(eval("2*1/2"))
sps = nmax+1
tr = square_lattice_trans(Lx,Ly)
basis_dict = {}
basis_dict_f = {}
basis_dict_combined = {}
Nups=range(nmax*N+1)
for Nup in Nups:
basis_blocks=[]
basis_blocks_f=[]
pcon_basis = spin_basis_general(N,Nup=Nup,pauli=False)
pcon_basis_f = spinful_fermion_basis_general(N,Nf=(Nup,N-Nup),double_occupancy=False)
Ns_block = 0
for blocks in tr.allowed_blocks_spin_inversion_iter(Nup,sps):
basis = spin_basis_general(N,Nup=Nup,pauli=False,**blocks)
Ns_block += basis.Ns
basis_blocks.append(basis)
Ns_block_f = 0
for blocks_f in tr.allowed_blocks_spin_inversion_iter(Nup,sps): # requires simple symmetry definition
basis_f = spinful_fermion_basis_general(N,Nf=(Nup,N-Nup),double_occupancy=False,**blocks_f)
Ns_block_f += basis_f.Ns
basis_blocks_f.append(basis_f)
try:
assert(Ns_block == pcon_basis.Ns)
except AssertionError:
print(Nup,Ns_block,pcon_basis.Ns)
raise AssertionError("reduced blocks don't sum to particle sector.")
try:
assert(Ns_block_f == pcon_basis_f.Ns)
except AssertionError:
print(Nup,Ns_block_f,pcon_basis_f.Ns)
raise AssertionError("fermion reduced blocks don't sum to particle sector.")
try:
assert(Ns_block == pcon_basis_f.Ns)
except AssertionError:
print(Nup,Ns_block_f,pcon_basis_f.Ns)
raise AssertionError("fermion reduced blocks don't match spin blocks.")
basis_dict[Nup] = (pcon_basis,basis_blocks)
basis_dict_f[Nup] = (pcon_basis_f,basis_blocks_f)
basis_dict_combined[Nup] = (pcon_basis,basis_blocks,pcon_basis_f,basis_blocks_f)
J = [[1.0,i,tr.T_x[i]] for i in range(N)] + [[1.0,i,tr.T_y[i]] for i in range(N)]
J_nn_ij = [[-0.25,i,tr.T_x[i]] for i in range(N)] + [[-0.25,i,tr.T_y[i]] for i in range(N)]
J_nn_ji = [[-0.25,tr.T_x[i],i] for i in range(N)] + [[-0.25,tr.T_y[i],i] for i in range(N)]
J_nn_ij_p = [[0.25,i,tr.T_x[i]] for i in range(N)] + [[0.25,i,tr.T_y[i]] for i in range(N)]
J_nn_ji_p = [[0.25,tr.T_x[i],i] for i in range(N)] + [[0.25,tr.T_y[i],i] for i in range(N)]
J_cccc_ij = [[-1.0,i,tr.T_x[i],tr.T_x[i],i] for i in range(N)] + [[-1.0,i,tr.T_y[i],tr.T_y[i],i] for i in range(N)]
J_cccc_ji = [[-1.0,tr.T_x[i],i,i,tr.T_x[i]] for i in range(N)] + [[-1.0,tr.T_y[i],i,i,tr.T_y[i]] for i in range(N)]
static = [["zz",J],["+-",J],["-+",J]]
static_f = [["nn|",J_nn_ij_p],["|nn",J_nn_ji_p],["n|n",J_nn_ij],["n|n",J_nn_ji],["+-|+-",J_cccc_ij],["+-|+-",J_cccc_ji]]
E_symm = {}
E_symm_f = {}
#'''
for N,(pcon_basis,basis_blocks,pcon_basis_f,basis_blocks_f) in basis_dict_combined.items():
H_pcon = hamiltonian(static,[],basis=pcon_basis,dtype=np.float64)
H_pcon_f = hamiltonian(static_f,[],basis=pcon_basis_f,dtype=np.float64)
if H_pcon.Ns>0:
E_pcon = np.linalg.eigvalsh(H_pcon.todense())
else:
E_pcon = np.array([])
if H_pcon_f.Ns>0:
E_pcon_f = np.linalg.eigvalsh(H_pcon_f.todense())
else:
E_pcon_f = np.array([])
E_block = []
E_block_f = []
for basis, basis_f in zip(basis_blocks,basis_blocks_f):
H = hamiltonian(static,[],basis=basis,dtype=np.complex128)
H_f = hamiltonian(static_f,[],basis=basis_f,dtype=np.complex128)
if H.Ns>0:
E_block.append(np.linalg.eigvalsh(H.todense()))
if H_f.Ns>0:
E_block_f.append(np.linalg.eigvalsh(H_f.todense()))
E_block = np.hstack(E_block)
E_block.sort()
E_block_f = np.hstack(E_block_f)
E_block_f.sort()
np.testing.assert_allclose(E_pcon,E_block,atol=1e-13)
np.testing.assert_allclose(E_pcon_f,E_block_f,atol=1e-13)
np.testing.assert_allclose(E_pcon,E_pcon_f,atol=1e-13)
print("passed N={} sector".format(N))
def test_gen_basis_spin(l_max,S="1/2"):
L=6
kblocks = [None]
kblocks.extend(range(L))
pblocks = [None,0,1]
zblocks = [None,0,1]
if S=="1/2":
ops = ["x","y","z","+","-","I"]
else:
ops = ["z","+","-","I"]
sps,s=S_dict[S]
Nups = [None,int(s*L)]
t = np.array([(i+1)%L for i in range(L)])
p = np.array([L-i-1 for i in range(L)])
z = np.array([-(i+1) for i in range(L)])
for Nup,kblock,pblock,zblock in product(Nups,kblocks,pblocks,zblocks):
gen_blocks = {"pauli":False,"S":S}
basis_blocks = {"pauli":False,"S":S}
if kblock==0 or kblock==L//2:
if pblock is not None:
basis_blocks["pblock"] = (-1)**pblock
gen_blocks["pblock"] = (p,pblock)
else:
basis_blocks["pblock"] = None
gen_blocks["pblock"] = None
else:
basis_blocks["pblock"] = None
gen_blocks["pblock"] = None
if zblock is not None:
basis_blocks["zblock"] = (-1)**zblock
gen_blocks["zblock"] = (z,zblock)
else:
basis_blocks["zblock"] = None
gen_blocks["zblock"] = None
if kblock is not None:
basis_blocks["kblock"] = kblock
gen_blocks["kblock"] = (t,kblock)
else:
basis_blocks["kblock"] = None
gen_blocks["kblock"] = None
basis_1d = spin_basis_1d(L,Nup=Nup,**basis_blocks)
gen_basis = spin_basis_general(L,Nup=Nup,**gen_blocks)
n = basis_1d._get_norms(np.float64)**2
n_gen = (gen_basis._n.astype(np.float64))*gen_basis._pers.prod()
if basis_1d.Ns != gen_basis.Ns:
print(L,basis_blocks)
print(basis_1d)
print(gen_basis)
raise ValueError("basis size mismatch")
try:
np.testing.assert_allclose(basis_1d._basis-gen_basis._basis,0,atol=1e-6)
np.testing.assert_allclose(n-n_gen ,0,atol=1e-6)
except:
print(basis_1d._basis)
print(gen_basis._basis)
print(n.shape)
print(n_gen.shape)
raise Exception
for l in range(1,l_max+1):
for i0 in range(0,L-l+1,1):
indx = range(i0,i0+l,1)
for opstr in product(*[ops for i in range(l)]):
opstr = "".join(list(opstr))
printing = dict(basis_blocks)
printing["opstr"]=opstr
printing["indx"]=indx
printing["Nup"]=Nup
printing["S"]=S
err_msg="testing: {opstr:} {indx:} S={S:} Nup={Nup:} kblock={kblock:} pblock={pblock:} zblock={zblock:}".format(**printing)
check_ME(basis_1d,gen_basis,opstr,indx,np.complex128,err_msg)
def check_gen_basis_hcb(S="1/2"):
L=6
kblocks = [None]
kblocks.extend(range(L))
pblocks = [None,0,1]
zblocks = [None,0,1]
sps,s=S_dict[S]
Nups = [None,int(s*L)]
t = np.array([(i+1)%L for i in range(L)])
p = np.array([L-i-1 for i in range(L)])
z = np.array([-(i+1) for i in range(L)])
for Nup,kblock,pblock,zblock in product(Nups,kblocks,pblocks,zblocks):
gen_blocks = {"S":S,"pauli":False}
basis_blocks = {"S":S,"pauli":False}
dtype=np.complex128
if kblock==0 or kblock==L//2:
if pblock is not None:
dtype=np.float64
basis_blocks["pblock"] = (-1)**pblock
gen_blocks["pblock"] = (p,pblock)
else:
basis_blocks["pblock"] = None
gen_blocks["pblock"] = None
else:
basis_blocks["pblock"] = None
gen_blocks["pblock"] = None
if zblock is not None:
basis_blocks["zblock"] = (-1)**zblock
gen_blocks["zblock"] = (z,zblock)
else:
basis_blocks["zblock"] = None
gen_blocks["zblock"] = None
if kblock is not None:
basis_blocks["kblock"] = kblock
gen_blocks["kblock"] = (t,kblock)
else:
basis_blocks["kblock"] = None
gen_blocks["kblock"] = None
print("checking S={S:} Nup={Nup:} kblock={kblock:} pblock={pblock:} zblock={zblock:}".format(Nup=Nup,**basis_blocks))
basis_1d = spin_basis_1d(L,Nup=Nup,**basis_blocks)
gen_basis = spin_basis_general(L,Nup=Nup,**gen_blocks)
P1 = basis_1d.get_proj(dtype)
P2 = gen_basis.get_proj(dtype)
np.testing.assert_allclose((P1-P2).data,0,atol=1e-14,err_msg="failed projector")
v = np.random.ranf(size=(basis_1d.Ns,)).astype(dtype)
vs = np.random.ranf(size=(basis_1d.Ns,100)).astype(dtype)
v1 = basis_1d.get_vec(v,sparse=False)
v2 = gen_basis.get_vec(v,sparse=False)
np.testing.assert_allclose((v1-v2),0,atol=1e-14,err_msg="failed single vector dense")
v1 = basis_1d.get_vec(v,sparse=True)
v2 = gen_basis.get_vec(v,sparse=True)
np.testing.assert_allclose((v1-v2).data,0,atol=1e-14,err_msg="failed single vector sparse")
vs1 = basis_1d.get_vec(vs,sparse=False)
vs2 = gen_basis.get_vec(vs,sparse=False)
np.testing.assert_allclose((vs1-vs2),0,atol=1e-14,err_msg="failed multi vector dense")
vs1 = basis_1d.get_vec(vs,sparse=True)
vs2 = gen_basis.get_vec(vs,sparse=True)
np.testing.assert_allclose((vs1-vs2).data,0,atol=1e-14,err_msg="failed multi vector sparse")
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) ) basis_spin_full = spin_basis_general(N_2d, pauli=False, make_basis=True, Nup=N_2d//2, ) basis_fermion = spinless_fermion_basis_general(N_2d, make_basis=False, Nf=N_2d//2, kxblock=(T_x,0),kyblock=(T_y,0), rblock=(R,0), pxblock=(P_x,0),pyblock=(P_y,0), )
else:
np.testing.assert_allclose(pm_1, ratio_12 * pm_2, atol=1e-13)
np.testing.assert_allclose(mp_1, ratio_12 * mp_2, atol=1e-13)
np.testing.assert_allclose(xx_1, ratio_12 * xx_2, atol=1e-13)
np.testing.assert_allclose(yy_1, ratio_12 * yy_2, atol=1e-13)
np.testing.assert_allclose(zz_1, ratio_12 * zz_2, atol=1e-13)
basis_1d_S = spin_basis_1d(L=L, pauli=0)
basis_1d_pauli_1 = spin_basis_1d(L=L)
basis_1d_pauli_2 = spin_basis_1d(L=L, pauli=-1)
spin_basis_general_S = spin_basis_general(N=L, pauli=0)
spin_basis_general_pauli_1 = spin_basis_general(N=L)
spin_basis_general_pauli_2 = spin_basis_general(N=L, pauli=-1)
bases = [(basis_1d_S, basis_1d_pauli_1, basis_1d_pauli_2),
(spin_basis_general_S, spin_basis_general_pauli_1,
spin_basis_general_pauli_2)]
no_checks = dict(check_herm=False,
check_pcon=False,
check_symm=False,
dtype=np.float64)
for basis_S, basis_pauli_1, basis_pauli_2 in bases:
# check Op and Op_bra_ket functions