def test_eigs_sparse_wvecs(self, mat_herm_sparse, backend):
u, a = mat_herm_sparse
assert qu.issparse(a)
lk, vk = qu.eigh(a, k=2, backend=backend)
assert_allclose(lk, (-3, -1))
for i, j in zip([3, 0], [0, 1]):
o = u[:, [i]].H @ vk[:, [j]]
assert_allclose(abs(o), 1.)
vk = qu.eigvecsh(a, k=2, backend=backend)
for i, j in zip([3, 0], [0, 1]):
o = u[:, [i]].H @ vk[:, [j]]
assert_allclose(abs(o), 1.)
def test_spin_half_double_space(self, sz):
prj = qu.zspin_projector(5, sz)
h = qu.ham_heis(5)
h0 = prj.T @ h @ prj
v0s = qu.eigvecsh(h0)
for v0 in v0s.T:
vf = prj @ v0.T
prjv = vf @ vf.H
# Check reconstructed full eigenvectors commute with full ham
assert_allclose(prjv @ h, h @ prjv, atol=1e-13)
if sz == 0:
# Groundstate must be in most symmetric subspace
gs = qu.groundstate(h)
gs0 = prj @ v0s[:, 0]
assert_allclose(qu.expec(gs, gs0), 1.0)
assert_allclose(qu.expec(h, gs0), qu.expec(h, gs))
def test_works(self, sz):
prj = qu.zspin_projector(4, sz)
h = qu.ham_heis(4)
h0 = prj.T @ h @ prj
v0s = qu.eigvecsh(h0)
for i in range(v0s.shape[1]):
v0 = v0s[:, [i]]
vf = prj @ v0
prjv = vf @ vf.H
# Check reconstructed full eigenvectors commute with full ham
assert_allclose(prjv @ h, h @ prjv, atol=1e-13)
if sz == 0:
# Groundstate must be in most symmetric subspace
gs = qu.groundstate(h)
gs0 = prj @ v0s[:, [0]]
assert_allclose(qu.expec(gs, gs0), 1.0)
assert_allclose(qu.expec(h, gs0), qu.expec(h, gs))
def test_eigvecs(self, mat_herm_dense):
u, a = mat_herm_dense
v = qu.eigvecsh(a)
for i, j in zip([3, 0, 1, 2], range(4)):
o = u[:, [i]].H @ v[:, [j]]
assert_allclose(abs(o), 1.)
if dis_flag == 1:
H_0 = qu.ham_mbl(N,
W_i,
J_tab,
cyclic=False,
dh_dist='qp',
beta=0.721,
seed=seed,
sparse=True).real
else:
H_0 = qu.ham_mbl(N, W_i, J_tab, cyclic=False, seed=seed, sparse=True).real
H_pre = P.T @ H_0 @ P
psi_0 = qu.eigvecsh(H_pre, k=1, which='SA').ravel()
if dis_flag == 1:
H_1 = qu.ham_mbl(N,
W,
J_tab,
cyclic=False,
dh_dist='qp',
beta=0.721,
seed=seed,
sparse=True).real
else:
H_1 = qu.ham_mbl(N, W, J_tab, cyclic=False, seed=seed, sparse=True).real
H_post = P.T @ H_1 @ P
def test_sparse(self):
a = qu.rand_herm(10, sparse=True, density=0.9)
vt = qu.eigvecsh(a, sigma=0, k=1)
assert qu.is_eigenvector(vt, a)
vf = qu.rand_ket(10)
assert not qu.is_eigenvector(vf, a)
def test_dense_true(self):
a = qu.rand_herm(10)
v = qu.eigvecsh(a)
for i in range(10):
assert qu.is_eigenvector(v[:, [i]], a)
def orthog_ks():
p = qu.rand_rho(3)
v = qu.eigvecsh(p)
return (v[:, [0]], v[:, [1]], v[:, [2]])
def orthog_ks():
p = qu.rand_rho(3)
v = qu.eigvecsh(p)
return (v[:, 0], v[:, 1], v[:, 2])
### Global parameters ###
N = params.L
W = params.D
J = 1.0
dis_flag = params.Dis_gen
seed = int(1000000 * np.random.random())
int_flag = 1
t_tab = np.logspace(-2, 1.5, 300)
### ETH ---> MBL ###
J_ETH = (J, J, J)
P = qu.zspin_projector(N, sz=0)
H_ETH = P.T @ qu.ham_heis(N, J_ETH, sparse=True, cyclic=False) @ P
Psi_ETH = qu.eigvecsh(H_ETH, k=1, which='SA')
J_evo1 = (0.0, 0.0, 0.0)
H_evo1 = P.T @ qu.ham_mbl(N,
W,
J_evo1,
cyclic=False,
dh_dist='qp',
beta=0.721,
seed=seed,
sparse=True).real @ P
compute = {
'time': lambda t, p: t,
'losch': lambda t, p: qu.fidelity(Psi_ETH, p)
}
