def test_canonical_form(bc, method):
psi = random_MPS(8, 2, 6, form=None, bc=bc)
psi2 = psi.copy()
norm = np.sqrt(psi2.overlap(psi2, ignore_form=True))
print("norm =", norm)
psi2.norm /= norm # normalize psi2
norm2 = psi.overlap(psi2, ignore_form=True)
print("norm2 =", norm2)
assert abs(norm2 - norm) < 1.e-14 * norm
meth = getattr(psi, method)
meth(renormalize=False) # psi.canonical_form_[infinite[2]]()
psi.test_sanity()
assert abs(psi.norm - norm) < 1.e-14 * norm
psi.norm = 1. # normalized psi
ov = psi.overlap(psi2, ignore_form=True)
print("normalized states: overlap <psi_canonical|psi> = 1.-", 1. - ov)
assert abs(ov - 1.) < 1.e-14
print("norm_test")
print(psi.norm_test())
assert np.max(psi.norm_test()) < 1.e-14 # SB = AS to good precision
psi3 = psi.copy()
# call canonical_form again, it shouldn't do anything now
meth(renormalize=True)
psi.test_sanity()
ov = psi.overlap(psi3)
assert abs(ov - 1.) < 1.e-14
if method in ['canonical_form_finite', 'canonical_form_infinite2']:
# check that A = SB S^-1 is orthonormal
for i in range(psi.L):
A = psi.get_B(i, 'A')
c = npc.tensordot(A, A.conj(), axes=[['vL', 'p'], ['vL*', 'p*']])
A_err = (c - npc.diag(1., c.legs[0])).norm()
print(A_err)
assert A_err < 1.e-13
def test_TransferMatrix(chi=4, d=2):
psi = random_MPS(2, d, chi, bc='infinite', form=None)
full_TM = npc.tensordot(psi._B[0], psi._B[0].conj(), axes=['p', 'p*'])
full_TM = npc.tensordot(full_TM, psi._B[1], axes=['vR', 'vL'])
full_TM = npc.tensordot(full_TM, psi._B[1].conj(), axes=[['vR*', 'p'], ['vL*', 'p*']])
full_TM = full_TM.combine_legs([['vL', 'vL*'], ['vR', 'vR*']], qconj=[+1, -1])
full_TM_dense = full_TM.to_ndarray()
eta_full, w_full = np.linalg.eig(full_TM_dense)
sort = np.argsort(np.abs(eta_full))[::-1]
eta_full = eta_full[sort]
w_full = w_full[:, sort]
TM = mps.TransferMatrix(psi, psi, charge_sector=0, form=None)
eta, w = TM.eigenvectors(3)
print("transfer matrix yields eigenvalues ", eta)
print(eta.shape, eta_full.shape)
print(psi.dtype)
# note: second and third eigenvalue are complex conjugates
if bool(eta[2].imag > 0.) == bool(eta_full[2].imag > 0.):
npt.assert_allclose(eta[:3], eta_full[:3])
else:
npt.assert_allclose(eta[:3], eta_full[:3].conj())
# compare largest eigenvector
w0_full = w_full[:, 0]
w0 = w[0].to_ndarray()
assert (abs(np.sum(w0_full)) > 1.e-20) # should be the case for random stuff
w0_full /= np.sum(w0_full) # fixes norm & phase
w0 /= np.sum(w0)
npt.assert_allclose(w0, w0_full)
def test_MPO_var(L=8, tol=1.e-13):
xxz_pars = dict(L=L,
Jx=1.,
Jy=1.,
Jz=1.1,
hz=0.1,
bc_MPS='finite',
conserve=None)
M = SpinChain(xxz_pars)
psi = random_MPS(L, 2, 10)
exp_val = M.H_MPO.expectation_value(psi)
ED = ExactDiag(M)
ED.build_full_H_from_mpo()
psi_full = ED.mps_to_full(psi)
exp_val_full = npc.inner(psi_full,
npc.tensordot(ED.full_H, psi_full, axes=1),
axes='range',
do_conj=True)
assert abs(exp_val - exp_val_full) / abs(exp_val_full) < tol
Hsquared = M.H_MPO.variance(psi, 0.)
Hsquared_full = npc.inner(psi_full,
npc.tensordot(ED.full_H,
npc.tensordot(ED.full_H,
psi_full,
axes=1),
axes=1),
axes='range',
do_conj=True)
assert abs(Hsquared - Hsquared_full) / abs(Hsquared_full) < tol
var = M.H_MPO.variance(psi)
var_full = Hsquared_full - exp_val_full**2
assert abs(var - var_full) / abs(var_full) < tol
def test_canonical_form(bc):
psi = random_MPS(8, 2, 6, form=None, bc=bc)
psi2 = psi.copy()
norm = np.sqrt(psi2.overlap(psi2, ignore_form=True))
print("norm =", norm)
psi2.norm /= norm # normalize psi2
norm2 = psi.overlap(psi2, ignore_form=True)
print("norm2 =", norm2)
assert abs(norm2 - norm) < 1.e-14 * norm
psi.canonical_form(renormalize=False)
psi.test_sanity()
assert abs(psi.norm - norm) < 1.e-14 * norm
psi.norm = 1. # normalized psi
ov = psi.overlap(psi2, ignore_form=True)
print("normalized states: overlap <psi_canonical|psi> = 1.-", 1. - ov)
assert abs(ov - 1.) < 1.e-14
print("norm_test")
print(psi.norm_test())
assert np.max(psi.norm_test()) < 1.e-14
