def test_tasep_mpo(self):
mpiprint(
0, '\n' + '=' * 50 +
'\nTesting Initial Environment Using TASEP MPO\n' + '-' * 50)
# Create an MPS
from cyclomps.tools.mps_tools import create_mps_list, make_mps_list_right, load_mps_list, calc_mps_norm
d = 2
N = 4
mbd = 10
nState = 4
mpsList = create_mps_list([d] * N, mbd, nState)
# Load the MPO
from cyclomps.mpo.tasep import return_mpo
mpo = return_mpo(N, (0.5, 0.5, 1.))
# Create a function to compute energy
def calc_energy(mps, mpo, load_mps=True):
if load_mps:
mps = load_mps_list(mps)
E = zeros(nState, dtype=mps[0][0].dtype)
for state in range(nState):
psi = einsum('apb,bqc,crd,dse->pqrs', mps[state][0],
mps[state][1], mps[state][2], mps[state][3])
op = einsum('iPpj,jQqk,kRrl,lSsm->PpQqRrSs', mpo[0][0],
mpo[0][1], mpo[0][2], mpo[0][3])
psi_conj = einsum('apb,bqc,crd,dse->pqrs', conj(mps[state][0]),
conj(mps[state][1]), conj(mps[state][2]),
conj(mps[state][3]))
E[state] = einsum('pqrs,PpQqRrSs,PQRS', psi, op, psi_conj)
norm = einsum('pqrs,pqrs->', psi, psi_conj)
E[state] /= norm
return E
# Compute energy
E1 = calc_energy(mpsList, mpo)
mpiprint(0, 'Initial Energy =\n{}'.format(E1))
# Right Canonicalize
mpsList = make_mps_list_right(mpsList)
# Compute energy again
E2 = calc_energy(mpsList, mpo)
mpiprint(0, 'Energy after canonicalization =\n{}'.format(E2))
# Calculate the environment
from cyclomps.tools.env_tools import calc_env, env_load_ten, load_env_list
envList = calc_env(mpsList, mpo)
# Calculate the energy using the environment
env = load_env_list(envList)
mps = load_mps_list(mpsList)
E3 = zeros(nState, dtype=mps[0][0].dtype)
for state in range(nState):
E3[state] = einsum('Ala,apb,lPpr,APB,Brb->', env[0][0], mps[0][0],
mpo[0][0], conj(mps[0][0]), env[0][1])
E3[state] /= calc_mps_norm(mpsList, state=state)
mpiprint(0, 'Energy from environment =\n{}'.format(E3))
# Check Results
self.assertTrue(summ(abss(E1[0] - E2[0])) < 1e-10)
self.assertTrue(summ(abss(E1[0] - E3[0])) < 1e-10)
mpiprint(0, 'Passed\n' + '=' * 50)
def calc_energy(mpsL, mpo):
mps = load_mps_list(mpsL)
E = zeros(nState, dtype=mps[0][0].dtype)
for state in range(nState):
psi = einsum('apb,bqc,crd,dse->pqrs', mps[state][0],
mps[state][1], mps[state][2], mps[state][3])
op = einsum('iPpj,jQqk,kRrl,lSsm->PpQqRrSs', mpo[0][0],
mpo[0][1], mpo[0][2], mpo[0][3])
psi_conj = einsum('apb,bqc,crd,dse->pqrs', conj(mps[state][0]),
conj(mps[state][1]), conj(mps[state][2]),
conj(mps[state][3]))
E[state] = einsum('pqrs,PpQqRrSs,PQRS', psi, op, psi_conj)
E[state] /= calc_mps_norm(mpsL, state=state)
return E
def test_renorm_avg_left_energy2(self):
mpiprint(
0, '\n' + '=' * 50 +
'\nTesting state avg left renormalization effect on Energy\n' +
'-' * 50)
from cyclomps.tools.mps_tools import create_mps_list, make_mps_list_left, load_mps_list, calc_mps_norm, move_gauge
from cyclomps.mpo.tasep import return_mpo
from cyclomps.algs.dmrg1 import renormalize_left
# Create an MPS
d = 2
N = 4
mbd = 10
nState = 4
mpsL = create_mps_list([d] * N, mbd, nState)
mpsL = make_mps_list_left(mpsL)
# Load the MPO
mpo = return_mpo(N, (0.5, 0.5, 1.))
# Create a function to compute energy
def calc_energy(mpsL, mpo, load_mps=True):
if load_mps:
mps = load_mps_list(mpsL)
else:
mps = mpsL
E = zeros(nState, dtype=mps[0][0].dtype)
for state in range(nState):
psi = einsum('apb,bqc,crd,dse->pqrs', mps[state][0],
mps[state][1], mps[state][2], mps[state][3])
op = einsum('iPpj,jQqk,kRrl,lSsm->PpQqRrSs', mpo[0][0],
mpo[0][1], mpo[0][2], mpo[0][3])
psi_conj = einsum('apb,bqc,crd,dse->pqrs', conj(mps[state][0]),
conj(mps[state][1]), conj(mps[state][2]),
conj(mps[state][3]))
E[state] = einsum('pqrs,PpQqRrSs,PQRS', psi, op, psi_conj)
return E
# Calc initial Energy
E1 = calc_energy(mpsL, mpo)
mps = load_mps_list(mpsL)
E1_ = calc_energy(mps, mpo, load_mps=False)
E1__ = calc_energy(mps, mpo, load_mps=False)
# Move gauge using renormalization
site = N - 1
(mps0, ) = retrieve_tensors(site - 1, mpsList=mpsL)
(mps1, ) = retrieve_tensors(site, mpsList=mpsL)
mps0_ = copy.deepcopy(mps0)
mps1_ = copy.deepcopy(mps1)
mps0, mps1, EE, EEs, wgt = renormalize_left(mps0, mps1, state_avg=True)
save_tensors(site - 1, mpsList=mpsL, mps=mps0)
save_tensors(site, mpsList=mpsL, mps=mps1)
# Check to make sure contracted states and local energies are the same
for state in range(nState):
finalState = einsum('apb,bqc->apqc', conj(mps0[state]),
conj(mps1[state]))
initState = einsum('apb,bqc->apqc', conj(mps0_[state]),
conj(mps1_[state]))
mpoComb = einsum('lPpm,mQqn->lPpQqn', mpo[0][site - 1],
mpo[0][site])
initLocalE = einsum('apqc,lPpQqn,APQC->AlaCnc', initState, mpoComb,
conj(initState))
finalLocalE = einsum('apqc,lPpQqn,APQC->AlaCnc', finalState,
mpoComb, conj(finalState))
self.assertTrue(summ(abss(finalState - initState)) < 1e-10)
self.assertTrue(summ(abss(initLocalE - initLocalE)) < 1e-10)
# Check to make sure we get the same energies from resulting states
for state in range(nState):
mps[state][site - 1] = mps0[state]
mps[state][site] = mps1[state]
# Calc Energy Again
E2 = calc_energy(mps, mpo, load_mps=False)
# Check Energies
self.assertTrue(summ(abss(E1[0] - E2[0])) < 1e-10)
self.assertTrue(summ(abss(E1[1] - E2[1])) < 1e-10)
self.assertTrue(summ(abss(E1[2] - E2[2])) < 1e-10)
self.assertTrue(summ(abss(E1[3] - E2[3])) < 1e-10)
# Check for correct canonical form
for state in range(nState):
eye_check = einsum('apb,cpb->ac', mps1[state], conj(mps1[state]))
eye_actual = eye(eye_check.shape[0])
self.assertTrue(summ(abss(eye_check - eye_actual)) < 1e-10)
mpiprint(0, 'Passed\n' + '=' * 50)