def test_pauli_dim3(self):
for dir in (1, 'x', 'X',
2, 'y', 'Y',
3, 'z', 'Z'):
x = pauli(dir, dim=3)
assert_allclose(eigvals(x), [-1, 0, 1],
atol=1e-15)
def test_approx_spectral_function_ptr_ppt_lin_op(self, fn_approx_rtol,
psi_abc, psi_ab, bsz):
fn, approx, rtol = fn_approx_rtol
rho_ab_ppt = partial_transpose(psi_abc.ptr(DIMS, [0, 1]), DIMS[:-1], 0)
actual_x = sum(fn(eigvals(rho_ab_ppt)))
lo = LazyPtrPptOperator(psi_abc, DIMS, sysa=0, sysb=1)
approx_x = approx_spectral_function(lo, fn, K=20, R=20, bsz=bsz)
assert_allclose(actual_x, approx_x, rtol=rtol)
def test_approx_spectral_function(self, fn_matrix_rtol, bsz, mpi):
fn, matrix, rtol = fn_matrix_rtol
a = matrix(2**7)
pos = fn == np.sqrt
actual_x = sum(fn(eigvals(a)))
approx_x = approx_spectral_function(a, fn, K=20, R=20, mpi=mpi,
pos=pos, bsz=bsz)
assert_allclose(actual_x, approx_x, rtol=rtol)
def test_approx_spectral_function_ptr_lin_op(self, fn_approx_rtol,
psi_abc, psi_ab, bsz):
fn, approx, rtol = fn_approx_rtol
sysa = [0, 1]
rho_ab = psi_abc.ptr(DIMS, sysa)
actual_x = sum(fn(eigvals(rho_ab)))
lo = LazyPtrOperator(psi_abc, DIMS, sysa)
approx_x = approx(lo, R=50, bsz=bsz)
assert_allclose(actual_x, approx_x, rtol=rtol)
def test_approx_spectral_function_with_v0(self, fn_matrix_rtol, bsz):
fn, matrix, rtol = fn_matrix_rtol
a = matrix(2**7)
actual_x = sum(fn(eigvals(a)))
# check un-normalized state work properly
v0 = (neel_state(7) + neel_state(7, down_first=True))
v0 = v0.A.reshape(-1)
pos = fn == np.sqrt
approx_x = approx_spectral_function(a, fn, K=20, v0=v0, pos=pos,
bsz=bsz)
assert_allclose(actual_x, approx_x, rtol=rtol)
def test_entanglement(self):
rho = rand_seperable([2, 3, 2], 10)
assert_almost_equal(tr(rho), 1.0)
assert isherm(rho)
assert logneg(rho, [2, 6]) < 1e-12
assert logneg(rho, [6, 2]) < 1e-12
rho_a = ptr(rho, [2, 3, 2], 1)
el = eigvals(rho_a)
assert np.all(el < 1 - 1e-12)
assert np.all(el > 1e-12)
def test_approx_spectral_subspaces_with_heis_partition(self, bsz):
h = ham_heis(10, sparse=True)
beta = 0.01
actual_Z = sum(np.exp(-beta * eigvals(h.A)))
approx_Z = tr_exp_approx(-beta * h, bsz=bsz)
assert_allclose(actual_Z, approx_Z, rtol=3e-2)
def test_eigvals(self, mat_herm_dense, bkd):
_, a = mat_herm_dense
evals = eigvals(a, backend=bkd)
assert_allclose(evals, [-3, -1, 2, 4])
def test_rank(self, bond_dim, cyclic):
psi = rand_matrix_product_state(2, 10, bond_dim, cyclic=cyclic)
rhoa = ptr(psi, [2] * 10, [0, 1, 2, 3])
el = eigvals(rhoa)
# bond_dim squared as cyclic mps is generated
assert sum(el > 1e-12) == bond_dim**(2 if cyclic else 1)
def test_ham_heis_bz(self):
h = ham_heis(2, cyclic=False, b=1)
evals = eigvals(h)
assert_allclose(evals, [-3 / 4, -3 / 4, 1 / 4, 5 / 4])
def test_ham_heis_2(self):
h = ham_heis(2, cyclic=False)
evals = eigvals(h)
assert_allclose(evals, [-0.75, 0.25, 0.25, 0.25])
gs = groundstate(h)
assert_allclose(expec(gs, singlet()), 1.)
def test_pauli_dim2(self):
for dir in (1, 'x', 'X',
2, 'y', 'Y',
3, 'z', 'Z'):
x = pauli(dir)
assert_allclose(eigvals(x), [-1, 1])
def test_spin_high(self, label, S):
D = int(2 * S + 1)
op = spin_operator(label, S)
assert_allclose(eigvals(op), np.linspace(-S, S, D), atol=1e-13)