def sweep_right_left_two(self):
"""Performs the sweep left->right of the second order TDVP scheme with two sites update.
Evolve from 0.5*dt
"""
theta_old = self.psi.get_theta(self.L - 1, 1)
for j in range(self.L - 2, -1, -1):
theta = npc.tensordot(theta_old, self.psi.get_B(j, form='A'),
('vL', 'vR'))
theta.ireplace_label('p0', 'p1')
theta.ireplace_label('p', 'p0')
#theta=self.psi.get_theta(j,2)
Lp = self.environment.get_LP(j)
Rp = self.environment.get_RP(j + 1)
W1 = self.environment.H.get_W(j)
W2 = self.environment.H.get_W(j + 1)
theta = self.update_theta_h2(Lp, Rp, theta, W1, W2,
-1j * 0.5 * self.dt)
theta = theta.combine_legs([['vL', 'p0'], ['vR', 'p1']],
qconj=[+1, -1])
# SVD and update environment
U, s, V, err, renorm = svd_theta(theta, self.trunc_params)
s = s / npc.norm(s)
U = U.split_legs('(vL.p0)')
U.ireplace_label('p0', 'p')
V = V.split_legs('(vR.p1)')
V.ireplace_label('p1', 'p')
self.psi.set_B(j, U, form='A')
self._del_correct(j)
self.psi.set_SR(j, s)
self.psi.set_B(j + 1, V, form='B')
self._del_correct(j + 1)
if j > 0:
# Apply expm (-dt H) for 1-site
theta = self.psi.get_theta(j, 1)
theta.ireplace_label('p0', 'p')
Lp = self.environment.get_LP(j)
Rp = self.environment.get_RP(j)
theta = self.update_theta_h1(Lp, Rp, theta, W1,
1j * 0.5 * self.dt)
theta_old = theta
theta.ireplace_label('p', 'p0')
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')
B_R = V.split_legs('(p1.vR)').ireplace_label('p1', 'p')
psi.set_B(i, A_L, form='A') # left-canonical form
psi.set_B(i + 1, B_R, form='B') # right-canonical form
print("finished")
B = psi.get_B(i, form='B')
Wml = Wm[i]
B = npc.tensordot(Wml, B, ['p*', 'p']) # wL wR p vL vR
B.itranspose(['vL', 'wL', 'p', 'vR', 'wR'])
B = B.combine_legs([('vL', 'wL'), ('vR', 'wR')], qconj=[1, -1])
B.iset_leg_labels(['vL', 'p', 'vR'])
psi.set_B(i, B, form=None)
psi.canonical_form() # to BBB...
# SVD compression
for i in range(L - 1):
theta = psi.get_theta(i, n=2)
theta = theta.combine_legs([('vL', 'p0'), ('p1', 'vR')],
qconj=[1, -1]) # vL.p0 p1.vR
A0, S1, B1, error, renorm = svd_theta(theta, {
'svd_min': cutoff,
'chi_max': chimax
})
psi.set_B(i, A0.split_legs().replace_label('p0', 'p'), form='A')
psi.set_SR(i, S1)
psi.set_B(i + 1, B1.split_legs().replace_label('p1', 'p'), form='B')
#Then put on spin down partons
site = SpinHalfFermionSite()
Aml = parton_hwf
chinfo, p_leg = site.leg.chinfo, site.leg
def Ws(Aml, m):
"MPO for d_m^\dag (spin down)"
