def test_purification_TEBD(L=3):
xxz_pars = dict(L=L, Jxx=1., Jz=3., hz=0., bc_MPS='finite')
M = XXZChain(xxz_pars)
for disent in [
None, 'backwards', 'min(None,last)-renyi', 'noise-norm',
'renyi-min(None,noise-renyi)'
]:
psi = purification_mps.PurificationMPS.from_infiniteT(
M.lat.mps_sites(), bc='finite')
TEBD_params = {
'trunc_params': {
'chi_max': 16,
'svd_min': 1.e-8
},
'disentangle': disent,
'dt': 0.1,
'verbose': 30,
'N_steps': 2
}
eng = PurificationTEBD(psi, M, TEBD_params)
eng.run()
N = psi.expectation_value('Id') # check normalization : <1> =?= 1
npt.assert_array_almost_equal_nulp(N, np.ones([L]), 100)
eng.run_imaginary(0.2)
N = psi.expectation_value('Id') # check normalization : <1> =?= 1
npt.assert_array_almost_equal_nulp(N, np.ones([L]), 100)
if disent == 'last-renyi':
eng.run_imaginary(0.3)
eng.disentangle_global()
def test_canoncial_purification(L=6, charge_sector=0, eps=1.e-14):
site = spin_half
psi = purification_mps.PurificationMPS.from_infiniteT_canonical(
[site] * L, [charge_sector])
psi.test_sanity()
total_psi = psi.get_theta(0, L).take_slice(0, 'vL').take_slice(0, 'vR')
total_psi.itranspose(['p' + str(i) for i in range(L)] +
['q' + str(i) for i in range(L)])
# note: don't `combine_legs`: it will permute the p legs differently than q due to charges
total_psi_dense = total_psi.to_ndarray().reshape(2**L, 2**L)
# now it should be diagonal
diag = np.diag(total_psi_dense)
assert np.all(
np.abs(total_psi_dense - np.diag(diag) < eps)) # is it diagonal?
# and the diagonal should be sqrt(L choose L//2) for states with fitting numbers
pref = 1. / scipy.special.comb(L, L // 2 + charge_sector)**0.5
Q_p = site.leg.to_qflat()[:, 0]
for i, entry in enumerate(diag):
Q_i = sum([Q_p[int(b)] for b in format(i, 'b').zfill(L)])
if Q_i == charge_sector:
assert abs(entry - pref) < eps
else:
assert abs(entry) < eps
# and one quick test of TEBD
xxz_pars = dict(L=L, Jxx=1., Jz=3., hz=0., bc_MPS='finite')
M = XXZChain(xxz_pars)
TEBD_params = {
'trunc_params': {
'chi_max': 16,
'svd_min': 1.e-8
},
'disentangle': None, # 'renyi' should work as well, 'backwards' not.
'dt': 0.1,
'N_steps': 2
}
eng = PurificationTEBD(psi, M, TEBD_params)
eng.run_imaginary(0.2)
eng.run()
N = psi.expectation_value('Id') # check normalization : <1> =?= 1
npt.assert_array_almost_equal_nulp(N, np.ones([L]), 100)