def test_expm(size=10):
ci = chinfo3
l = gen_random_legcharge(ci, size)
A = npc.Array.from_func(np.random.random, [l, l.conj()], qtotal=None, shape_kw='size')
A_flat = A.to_ndarray()
exp_A = npc.expm(A)
exp_A.test_sanity()
from scipy.linalg import expm
npt.assert_array_almost_equal_nulp(expm(A_flat), exp_A.to_ndarray(), size * size)
print("H2 labels:", H2.get_leg_labels())
print("6) calculate exp(H2) by diagonalization of H2")
# diagonalization requires to view H2 as a matrix
H2 = H2.combine_legs([('p0', 'p1'), ('p0*', 'p1*')], qconj=[+1, -1])
print("labels after combine_legs:", H2.get_leg_labels())
E2, U2 = npc.eigh(H2)
print("Eigenvalues of H2:", E2)
U_expE2 = U2.scale_axis(np.exp(-1.j * dt * E2), axis=1) # scale_axis ~= apply a diagonal matrix
exp_H2 = npc.tensordot(U_expE2, U2.conj(), axes=(1, 1))
exp_H2.iset_leg_labels(H2.get_leg_labels())
exp_H2 = exp_H2.split_legs() # by default split all legs which are `LegPipe`
# (this restores the originial labels ['p0', 'p1', 'p0*', 'p1*'] of `H2` in `exp_H2`)
# alternative way: use :func:`~tenpy.linalg.np_conserved.expm`
exp_H2_alternative = npc.expm(-1.j * dt * H2).split_legs()
assert (npc.norm(exp_H2_alternative - exp_H2) < 1.e-14)
print("7) apply exp(H2) to even/odd bonds of the MPS and truncate with svd")
# (this implements one time step of first order TEBD)
trunc_par = {'svd_min': cutoff, 'trunc_cut': None, 'verbose': 0}
for even_odd in [0, 1]:
for i in range(even_odd, L - 1, 2):
theta = psi.get_theta(i, 2) # handles canonical form (i.e. scaling with 'S')
theta = npc.tensordot(exp_H2, theta, axes=(['p0*', 'p1*'], ['p0', 'p1']))
# view as matrix for SVD
theta = theta.combine_legs([('vL', 'p0'), ('p1', 'vR')], new_axes=[0, 1], qconj=[+1, -1])
# now theta has labels '(vL.p0)', '(p1.vR)'
U, S, V, err, invsq = svd_theta(theta, trunc_par, inner_labels=['vR', 'vL'])
psi.set_SR(i, S)
A_L = U.split_legs('(vL.p0)').ireplace_label('p0', 'p')
