def update_bond(self, i):
j = (i + 1) % self.psi.L
# get effective Hamiltonian
Heff = SimpleHeff(self.LPs[i], self.RPs[j], self.H_mpo[i],
self.H_mpo[j])
# Diagonalize Heff, find ground state `theta`
theta0 = np.reshape(self.psi.get_theta2(i),
[Heff.shape[0]]) # initial guess
e, v = arp.eigsh(Heff,
k=1,
which='SA',
return_eigenvectors=True,
v0=theta0)
theta = np.reshape(v[:, 0], Heff.theta_shape)
# split and truncate
Ai, Sj, Bj = split_truncate_theta(theta, self.chi_max, self.eps)
# put back into MPS
Gi = np.tensordot(np.diag(self.psi.Ss[i]**(-1)), Ai,
axes=[1, 0]) # vL [vL*], [vL] i vC
self.psi.Bs[i] = np.tensordot(Gi, np.diag(Sj),
axes=[2, 0]) # vL i [vC], [vC*] vC
self.psi.Ss[j] = Sj # vC
self.psi.Bs[j] = Bj # vC j vR
self.update_LP(i)
self.update_RP(j)
def run_infinite_TEBD(psi, U_bonds, N_steps, chi_max, eps=1.e-10):
"""basically the same as c_tebd.run_TEBD, but adjusted to work for infinite (uniform) MPS.
(should work regardless of whether you did exercise 10.1)"""
Nbonds = L = 2
for n in range(N_steps):
for k in [0, 1]: # even, odd
for i_bond in range(k, Nbonds, 2):
U_bond = U_bonds[i_bond]
i, j = i_bond, (i_bond + 1) % L
theta = psi.get_theta1(i)
theta = np.tensordot(theta, psi.Bs[j],
[2, 0]) # vL i [vR], [vL] j vR
Utheta = np.tensordot(
U_bond, theta,
axes=([2, 3], [1, 2])) # i j [i*] [j*], vL [i] [j] vR
Utheta = np.transpose(Utheta, [2, 0, 1, 3]) # vL i j vR
# split and truncate
Ai, Sj, Bj = split_truncate_theta(Utheta, chi_max, eps)
# put back into MPS
Gi = np.tensordot(np.diag(psi.Ss[i]**(-1)), Ai,
axes=[1, 0]) # vL [vL*], [vL] i vC
psi.Bs[i] = np.tensordot(Gi, np.diag(Sj),
axes=[2, 0]) # vL i [vC], [vC] vC
psi.Ss[j] = Sj # vC
psi.Bs[j] = Bj # vC j vR
def update_bond(psi, i, U_bond, chi_max, eps):
"""Apply `U_bond` acting on i,j=(i+1) to `psi`."""
j = (i + 1) % psi.L
# construct theta matrix
theta = psi.get_theta2(i) # vL i j vR
# apply U
Utheta = np.tensordot(U_bond, theta, axes=([2, 3], [1, 2])) # i j [i*] [j*], vL [i] [j] vR
Utheta = np.transpose(Utheta, [2, 0, 1, 3]) # vL i j vR
# split and truncate
Ai, Sj, Bj = split_truncate_theta(Utheta, chi_max, eps)
# put back into MPS
Gi = np.tensordot(np.diag(psi.Ss[i]**(-1)), Ai, axes=[1, 0]) # vL [vL*], [vL] i vC
psi.Bs[i] = np.tensordot(Gi, np.diag(Sj), axes=[2, 0]) # vL i [vC], [vC] vC
psi.Ss[j] = Sj # vC
psi.Bs[j] = Bj # vC j vR
def update_bond(self, i):
j = i + 1
# get effective Hamiltonian
Heff = HEffective(self.LPs[i], self.RPs[j], self.H_mpo[i], self.H_mpo[j])
# Diagonalize Heff, find ground state `theta`
theta0 = np.reshape(self.psi.get_theta2(i), [Heff.shape[0]]) # initial guess
e, v = arp.eigsh(Heff, k=1, which='SA', return_eigenvectors=True, v0=theta0)
theta = np.reshape(v[:, 0], Heff.theta_shape)
# split and truncate
Ai, Sj, Bj = split_truncate_theta(theta, self.chi_max, self.eps)
# put back into MPS
Gi = np.tensordot(np.diag(self.psi.Ss[i]**(-1)), Ai, axes=[1, 0]) # vL [vL*], [vL] i vC
self.psi.Bs[i] = np.tensordot(Gi, np.diag(Sj), axes=[2, 0]) # vL i [vC], [vC*] vC
self.psi.Ss[j] = Sj # vC
self.psi.Bs[j] = Bj # vC j vR
self.update_LP(i)
self.update_RP(j)
def run_infinite_TEBD(psi, U_bonds, N_steps, chi_max, eps=1.e-10):
"""basically the same as c_tebd.run_TEBD, but adjusted to work for infinite (uniform) MPS.
(should work regardless of whether you did exercise 10.1)"""
Nbonds = L = 2
for n in range(N_steps):
for k in [0, 1]: # even, odd
for i_bond in range(k, Nbonds, 2):
U_bond = U_bonds[i_bond]
i, j = i_bond, (i_bond + 1) % L
theta = psi.get_theta1(i)
theta = np.tensordot(theta, psi.Bs[j], [2, 0]) # vL i [vR], [vL] j vR
Utheta = np.tensordot(U_bond, theta, axes=([2, 3], [1, 2])) # i j [i*] [j*], vL [i] [j] vR
Utheta = np.transpose(Utheta, [2, 0, 1, 3]) # vL i j vR
# split and truncate
Ai, Sj, Bj = split_truncate_theta(Utheta, chi_max, eps)
# put back into MPS
Gi = np.tensordot(np.diag(psi.Ss[i]**(-1)), Ai, axes=[1, 0]) # vL [vL*], [vL] i vC
psi.Bs[i] = np.tensordot(Gi, np.diag(Sj), axes=[2, 0]) # vL i [vC], [vC] vC
psi.Ss[j] = Sj # vC
psi.Bs[j] = Bj # vC j vR
