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 make_environment(psi, H, N=5):
IdL = H.get_IdL(0)
assert IdL is not None
IdR = H.get_IdR(-1)
assert IdR is not None
vL = psi.get_B(0, None).get_leg('vL')
vR = psi.get_B(0, None).get_leg('vR')
wL = H.get_W(0).get_leg('wL')
wR = wL.conj()
dtype = psi.dtype
LP = npc.diag(1., vR, dtype=dtype, labels=['vR*', 'vR'])
LP = LP.add_leg(wR, IdL, axis=1, label='wR')
RP = npc.diag(1., vL, dtype=dtype, labels=['vL*', 'vL'])
RP = RP.add_leg(wL, IdR, axis=1, label='wL')
A = psi.get_B(0, form='A')
B = psi.get_B(0, form='B')
W = H.get_W(0)
TA = npc.tensordot(A, W, axes=('p', 'p'))
TA = npc.tensordot(A.conj(), TA, axes=('p*', 'p*')).itranspose(
['vL*', 'vR*', 'wL', 'wR', 'vL', 'vR'])
TB = npc.tensordot(B, W, axes=('p', 'p'))
TB = npc.tensordot(B.conj(), TB, axes=('p*', 'p*')).itranspose(
['vL*', 'vR*', 'wL', 'wR', 'vL', 'vR'])
for i in range(N):
LP = npc.tensordot(LP,
TA,
axes=(['vR', 'wR', 'vR*'], ['vL', 'wL', 'vL*']))
RP = npc.tensordot(RP,
TB,
axes=(['vL', 'wL', 'vL*'], ['vR', 'wR', 'vR*']))
return LP, RP
def test_lanczos_evolve(n, N_cache, tol=5.e-15):
# generate Hermitian test array
leg = gen_random_legcharge(ch, n)
H = npc.Array.from_func_square(rmat.GUE, leg) - npc.diag(1., leg)
H_flat = H.to_ndarray()
H_Op = H # use `matvec` of the array
qtotal = leg.to_qflat()[0]
psi_init = npc.Array.from_func(np.random.random, [leg], qtotal=qtotal)
psi_init /= npc.norm(psi_init)
psi_init_flat = psi_init.to_ndarray()
lanc = lanczos.LanczosEvolution(H_Op, psi_init, {
'verbose': 1,
'N_cache': N_cache
})
for delta in [-0.1j, 0.1j, 1.j]: #, 0.1, 1.]:
psi_final_flat = expm(H_flat * delta).dot(psi_init_flat)
psi_final, N = lanc.run(delta)
ov = np.inner(psi_final.to_ndarray().conj(), psi_final_flat)
ov /= np.linalg.norm(psi_final_flat)
print("<psi1|psi1_flat>/norm=", ov)
assert (abs(1. - abs(ov)) < tol)
def test_lanczos_evolve(n, N_cache, tol=5.e-14):
# generate Hermitian test array
leg = gen_random_legcharge(ch, n)
H = npc.Array.from_func_square(rmat.GUE, leg) - npc.diag(1., leg)
H_flat = H.to_ndarray()
H_Op = H # use `matvec` of the array
qtotal = leg.to_qflat()[0]
psi_init = npc.Array.from_func(np.random.random, [leg], qtotal=qtotal)
#psi_init /= npc.norm(psi_init) # not necessary
psi_init_flat = psi_init.to_ndarray()
lanc = lanczos.LanczosEvolution(H_Op, psi_init, {'N_cache': N_cache})
for delta in [-0.1j, 0.1j, 1.j, 0.1, 1.]:
psi_final_flat = expm(H_flat * delta).dot(psi_init_flat)
norm = np.linalg.norm(psi_final_flat)
psi_final, N = lanc.run(delta, normalize=False)
diff = np.linalg.norm(psi_final.to_ndarray() - psi_final_flat)
print("norm(|psi_final> - |psi_final_flat>)/norm = ",
diff / norm) # should be 1.
assert diff / norm < tol
psi_final2, N = lanc.run(delta, normalize=True)
assert npc.norm(psi_final / norm - psi_final2) < tol
W.iset_leg_labels(['wL', 'wR', 'p',
'p*']) # wL/wR = virtual left/right of the MPO
Ws = [W] * L
print("3) define 'environments' left and right")
# .---->- vR vL ->----.
# | |
# envL->- wR wL ->-envR
# | |
# .---->- vR* vL*->----.
envL = npc.zeros(
[W.get_leg('wL').conj(), Bs[0].get_leg('vL').conj(), Bs[0].get_leg('vL')])
envL.iset_leg_labels(['wR', 'vR', 'vR*'])
envL[0, :, :] = npc.diag(1., envL.legs[1])
envR = npc.zeros([
W.get_leg('wR').conj(), Bs[-1].get_leg('vR').conj(), Bs[-1].get_leg('vR')
])
envR.iset_leg_labels(['wL', 'vL', 'vL*'])
envR[-1, :, :] = npc.diag(1., envR.legs[1])
print("4) contract MPS and MPO to calculate the energy <psi|H|psi>")
contr = envL
for i in range(L):
# contr labels: wR, vR, vR*
contr = npc.tensordot(contr, Bs[i], axes=('vR', 'vL'))
# wR, vR*, vR, p
contr = npc.tensordot(contr, Ws[i], axes=(['p', 'wR'], ['p*', 'wL']))
# vR*, vR, wR, p
contr = npc.tensordot(contr,