def test_time_methods(algorithm):
L = 6
g = 1.2
model_params = dict(L=L, J=1., g=g, bc_MPS='finite', conserve=None)
M = TFIChain(model_params)
product_state = ["up"] * L #prepare system in spin polarized state
psi = MPS.from_product_state(M.lat.mps_sites(),
product_state,
bc=M.lat.bc_MPS)
dt = 0.01
N_steps = 2
t = 0.5 #total time evolution
params = {
'order': 2,
'dt': dt,
'N_steps': N_steps,
'trunc_params': {
'chi_max': 50,
'svd_min': 1.e-10,
'trunc_cut': None
}
}
if algorithm == 'TEBD':
eng = tebd.TEBDEngine(psi, M, params)
elif algorithm == 'TDVP':
params['active_sites'] = 2
del params['order']
eng = tdvp.TDVPEngine(psi, M, params)
elif algorithm == 'ExpMPO':
params['compression_method'] = 'SVD'
del params['order']
eng = mpo_evolution.ExpMPOEvolution(psi, M, params)
else:
raise ValueError("test works only for TEDB and TDVP so far")
mag = [psi.expectation_value("Sigmaz")]
szsz = [psi.correlation_function("Sigmaz", "Sigmaz")]
corr = psi.correlation_function("Sp", "Sm")
spsm = [corr.diagonal(1) + corr.diagonal(-1)]
for ti in np.arange(0, t, dt * N_steps):
eng.run()
mag.append(psi.expectation_value("Sigmaz"))
szsz.append(psi.correlation_function("Sigmaz", "Sigmaz"))
corr = psi.correlation_function("Sp", "Sm")
spsm.append(corr.diagonal(1) + corr.diagonal(-1))
m_exact, szsz_exact, spsm_exact = exact_expectation(L, g, t, dt * N_steps)
npt.assert_almost_equal(np.array(mag)[:-1, :], m_exact, 4)
npt.assert_almost_equal(np.array(szsz)[:-1, :, :], szsz_exact, 4)
npt.assert_almost_equal(np.array(spsm)[:-1, :], spsm_exact, 4)
def setup_benchmark(mod_q=[1], legs=10, size=20, **kwargs):
"""Setup TEBD benchmark.
Mapping of parameters:
size -> chi
legs -> L = number of sites
mod_q -> conserve
"""
L = legs # number of sites: legs is abbreviated with `l`
if len(mod_q) == 0:
conserve = None
elif mod_q == [2]:
conserve = 'parity'
elif mod_q == [1]:
conserve = 'Sz'
model_params = dict(L=L,
S=2.,
D=0.3,
bc_MPS='infinite',
conserve=conserve,
verbose=0)
# print("conserve =", repr(conserve))
M = SpinChain(model_params)
initial_state = (['up', 'down'] * L)[:L]
psi = MPS.from_product_state(M.lat.mps_sites(),
initial_state,
bc='infinite')
local_dim = psi.sites[0].dim
tebd_params = {
'trunc_params': {
'chi_max': size,
'svd_min': 1.e-45,
},
'order': 2,
'N_steps': 5,
'dt': 0.1,
'verbose': 0.,
}
eng = tebd.TEBDEngine(psi, M, tebd_params)
eng.verbose = 0.02
optimization.set_level(3)
for i in range(5 + int(np.log(size) / np.log(local_dim))):
eng.run()
if eng.verbose > 0.1:
print(eng.psi.chi)
print(eng.psi.entanglement_entropy())
assert min(eng.psi.chi) == size # ensure full bond dimension
if eng.verbose > 0.1:
print("set up tebd for size", size)
return eng
def example_TEBD_tf_ising_lightcone(L, g, tmax, dt):
print("finite TEBD, real time evolution")
print("L={L:d}, g={g:.2f}, tmax={tmax:.2f}, dt={dt:.3f}".format(L=L,
g=g,
tmax=tmax,
dt=dt))
# find ground state with TEBD or DMRG
# E, psi, M = example_TEBD_gs_tf_ising_finite(L, g)
from d_dmrg import example_DMRG_tf_ising_finite
print("(run DMRG to get the groundstate)")
E, psi, M = example_DMRG_tf_ising_finite(L, g)
print("(DMRG finished)")
i0 = L // 2
# apply sigmaz on site i0
psi.apply_local_op(i0, 'Sigmaz', unitary=True)
dt_measure = 0.05
# tebd.TEBDEngine makes 'N_steps' steps of `dt` at once;
# for second order this is more efficient.
tebd_params = {
'order': 2,
'dt': dt,
'N_steps': int(dt_measure / dt + 0.5),
'trunc_params': {
'chi_max': 50,
'svd_min': 1.e-10,
'trunc_cut': None
},
}
eng = tebd.TEBDEngine(psi, M, tebd_params)
S = [psi.entanglement_entropy()]
for n in range(int(tmax / dt_measure + 0.5)):
eng.run()
S.append(psi.entanglement_entropy())
import matplotlib.pyplot as plt
plt.figure()
plt.imshow(S[::-1],
vmin=0.,
aspect='auto',
interpolation='nearest',
extent=(0, L - 1., -0.5 * dt_measure,
eng.evolved_time + 0.5 * dt_measure))
plt.xlabel('site $i$')
plt.ylabel('time $t/J$')
plt.ylim(0., tmax)
plt.colorbar().set_label('entropy $S$')
filename = 'c_tebd_lightcone_{g:.2f}.pdf'.format(g=g)
plt.savefig(filename)
print("saved " + filename)
def example_TEBD_gs_tf_ising_finite(L, g):
print("finite TEBD, imaginary time evolution, transverse field Ising")
print("L={L:d}, g={g:.2f}".format(L=L, g=g))
model_params = dict(L=L, J=1., g=g, bc_MPS='finite', conserve=None)
M = TFIChain(model_params)
product_state = ["up"] * M.lat.N_sites
psi = MPS.from_product_state(M.lat.mps_sites(),
product_state,
bc=M.lat.bc_MPS)
tebd_params = {
'order': 2,
'delta_tau_list': [0.1, 0.01, 0.001, 1.e-4, 1.e-5],
'N_steps': 10,
'max_error_E': 1.e-6,
'trunc_params': {
'chi_max': 30,
'svd_min': 1.e-10
},
}
eng = tebd.TEBDEngine(psi, M, tebd_params)
eng.run_GS() # the main work...
# expectation values
E = np.sum(M.bond_energies(
psi)) # M.bond_energies() works only a for NearestNeighborModel
# alternative: directly measure E2 = np.sum(psi.expectation_value(M.H_bond[1:]))
print("E = {E:.13f}".format(E=E))
print("final bond dimensions: ", psi.chi)
mag_x = np.sum(psi.expectation_value("Sigmax"))
mag_z = np.sum(psi.expectation_value("Sigmaz"))
print("magnetization in X = {mag_x:.5f}".format(mag_x=mag_x))
print("magnetization in Z = {mag_z:.5f}".format(mag_z=mag_z))
if L < 20: # compare to exact result
from tfi_exact import finite_gs_energy
E_exact = finite_gs_energy(L, 1., g)
print("Exact diagonalization: E = {E:.13f}".format(E=E_exact))
print("relative error: ", abs((E - E_exact) / E_exact))
return E, psi, M
def example_TEBD_gs_tf_ising_infinite(g):
print("infinite TEBD, imaginary time evolution, transverse field Ising")
print("g={g:.2f}".format(g=g))
model_params = dict(L=2, J=1., g=g, bc_MPS='infinite', conserve=None)
M = TFIChain(model_params)
product_state = ["up"] * M.lat.N_sites
psi = MPS.from_product_state(M.lat.mps_sites(),
product_state,
bc=M.lat.bc_MPS)
tebd_params = {
'order': 2,
'delta_tau_list': [0.1, 0.01, 0.001, 1.e-4, 1.e-5],
'N_steps': 10,
'max_error_E': 1.e-8,
'trunc_params': {
'chi_max': 30,
'svd_min': 1.e-10
},
}
eng = tebd.TEBDEngine(psi, M, tebd_params)
eng.run_GS() # the main work...
E = np.mean(M.bond_energies(
psi)) # M.bond_energies() works only a for NearestNeighborModel
# alternative: directly measure E2 = np.mean(psi.expectation_value(M.H_bond))
print("E (per site) = {E:.13f}".format(E=E))
print("final bond dimensions: ", psi.chi)
mag_x = np.mean(psi.expectation_value("Sigmax"))
mag_z = np.mean(psi.expectation_value("Sigmaz"))
print("<sigma_x> = {mag_x:.5f}".format(mag_x=mag_x))
print("<sigma_z> = {mag_z:.5f}".format(mag_z=mag_z))
print("correlation length:", psi.correlation_length())
# compare to exact result
from tfi_exact import infinite_gs_energy
E_exact = infinite_gs_energy(1., g)
print("Analytic result: E (per site) = {E:.13f}".format(E=E_exact))
print("relative error: ", abs((E - E_exact) / E_exact))
return E, psi, M
def test_tdvp():
L = 10
J = 1
chi = 20
delta_t = 0.01
parameters = {
'L': L,
'S': 0.5,
'conserve': 'Sz',
'Jz': 1.0,
'Jy': 1.0,
'Jx': 1.0,
'hx': 0.0,
'hy': 0.0,
'hz': 0.0,
'muJ': 0.0,
'bc_MPS': 'finite',
}
heisenberg = tenpy.models.spins.SpinChain(parameters)
H_MPO = heisenberg.H_MPO
h_test = []
for i_sites in range(H_MPO.L):
h_test.append(
H_MPO.get_W(i_sites).transpose(['wL', 'wR', 'p*',
'p']).to_ndarray())
def random_prod_state_tenpy(L, a_model):
product_state = []
#the numpy mps used to compare
psi_compare = []
sz = 2. * np.random.randint(0, 2, size=L) - 1.0
for i in range(L):
psi_compare.append(np.zeros((2, 1, 1)))
if sz[i] > 0:
product_state += ["up"]
psi_compare[-1][0, 0, 0] = 1
else:
product_state += ["down"]
psi_compare[-1][1, 0, 0] = 1
psi = MPS.from_product_state(a_model.lat.mps_sites(),
product_state,
bc=a_model.lat.bc_MPS,
form='B')
psi_converted = []
for i in range(L):
site = psi.sites[i]
perm = site.perm
B_tmp = psi.get_B(i).transpose(['p', 'vL', 'vR']).to_ndarray()
B = B_tmp[inverse_permutation(perm), :, :]
B = B[::-1, :, :]
psi_converted.append(B)
return psi
psi = random_prod_state_tenpy(heisenberg.lat.N_sites, heisenberg)
N_steps = 50
tebd_params = {
'order': 2,
'dt': delta_t,
'N_steps': N_steps,
'trunc_params': {
'chi_max': 50,
'svd_min': 1.e-10,
'trunc_cut': None
}
}
tdvp_params = {
'start_time': 0,
'dt': delta_t,
'N_steps': N_steps,
'trunc_params': {
'chi_max': 50,
'svd_min': 1.e-10,
'trunc_cut': None
}
}
psi_tdvp2 = copy.deepcopy(psi)
engine = tebd.TEBDEngine(psi, heisenberg, tebd_params)
tdvp_engine = tdvp.TDVPEngine(psi_tdvp2, heisenberg, tdvp_params)
engine.run()
tdvp_engine.run_two_sites(N_steps)
ov = psi.overlap(psi_tdvp2)
print("overlap TDVP and TEBD")
psi = engine.psi
print("difference")
print(np.abs(1 - np.abs(ov)))
assert np.abs(1 - np.abs(ov)) < 1e-10
print("two sites tdvp works")
# test that the initial conditions are the same
tdvp_engine = tdvp.TDVPEngine(psi, heisenberg, tdvp_params)
psit_compare = []
for i in range(L):
B_tmp = psi.get_B(i).transpose(['p', 'vL', 'vR']).to_ndarray()
B = B_tmp[::-1, :, :]
psit_compare.append(B)
#**********************************************************************************************************
#Initialize TDVP
tdvp_params = {
'start_time': 0,
'dt': delta_t,
'N_steps': 1,
}
tdvp_engine = tdvp.TDVPEngine(psi, heisenberg, tdvp_params)
for t in range(10):
tdvp_engine.run_one_site(N_steps=1)
psit_compare, Rp_list, spectrum = tdvp_numpy.tdvp(psit_compare,
h_test,
0.5 * 1j * delta_t,
Rp_list=None)
psit_ = []
for i in range(L):
B = psi.get_B(i).transpose(['p', 'vL', 'vR']).to_ndarray()
B = B[::-1, :, :]
psit_.append(B)
assert np.abs(np.abs(overlap(psit_, psit_compare)) - 1.0) < 1e-13
print("one site TDVP works")
"""Call of (infinite) TEBD."""
from tenpy.networks.mps import MPS
from tenpy.models.tf_ising import TFIChain
from tenpy.algorithms import tebd
M = TFIChain({"L": 2, "J": 1., "g": 1.5, "bc_MPS": "infinite"})
psi = MPS.from_product_state(M.lat.mps_sites(), [0] * 2, "infinite")
tebd_params = {
"order": 2,
"delta_tau_list": [0.1, 0.001, 1.e-5],
"max_error_E": 1.e-6,
"trunc_params": {
"chi_max": 30,
"svd_min": 1.e-10
}
}
eng = tebd.TEBDEngine(psi, M, tebd_params)
eng.run_GS() # imaginary time evolution with TEBD
print("E =", sum(psi.expectation_value(M.H_bond)) / psi.L)
print("final bond dimensions: ", psi.chi)
def test_ExpMPOEvolution(bc_MPS, approximation, compression, g=1.5):
# Test a time evolution against exact diagonalization for finite bc
dt = 0.01
if bc_MPS == 'finite':
L = 6
else:
L = 2
# model_pars = dict(L=L, Jx=0., Jy=0., Jz=-4., hx=2. * g, bc_MPS=bc_MPS, conserve=None)
# state = ([[1 / np.sqrt(2), -1 / np.sqrt(2)]] * L) # pointing in (-x)-direction
# state = ['up'] * L # pointing in (-z)-direction
model_pars = dict(L=L,
Jx=1.,
Jy=1.,
Jz=1.,
hz=0.2,
bc_MPS=bc_MPS,
conserve='best')
state = ['up', 'down'] * (L // 2) # Neel
M = SpinChain(model_pars)
psi = MPS.from_product_state(M.lat.mps_sites(), state, bc=bc_MPS)
options = {
'dt': dt,
'N_steps': 1,
'order': 1,
'approximation': approximation,
'compression_method': compression,
'trunc_params': {
'chi_max': 30,
'svd_min': 1.e-8
}
}
eng = mpo_evolution.ExpMPOEvolution(psi, M, options)
if bc_MPS == 'finite':
ED = exact_diag.ExactDiag(M)
ED.build_full_H_from_mpo()
ED.full_diagonalization()
psiED = ED.mps_to_full(psi)
psiED /= psiED.norm()
UED = ED.exp_H(dt)
for i in range(30):
psi = eng.run()
psiED = npc.tensordot(UED, psiED, ('ps*', [0]))
psi_full = ED.mps_to_full(psi)
assert (abs(abs(npc.inner(psiED, psi_full, [0, 0], True)) - 1) <
dt)
if bc_MPS == 'infinite':
psiTEBD = psi.copy()
TEBD_params = {
'dt': dt,
'order': 2,
'N_steps': 1,
'trunc_params': options['trunc_params']
}
EngTEBD = tebd.TEBDEngine(psiTEBD, M, TEBD_params)
for i in range(30):
EngTEBD.run()
psi = eng.run()
# print(psi.norm)
print(abs(abs(psi.overlap(psiTEBD)) - 1),
abs(psi.overlap(psiTEBD) - 1))
assert (abs(abs(psi.overlap(psiTEBD)) - 1) < 1e-4)
def solve(self, model_params, psi):
M = TFIChain(model_params)
eng = tebd.TEBDEngine(psi, M, self.options)
eng.run_GS()
return np.mean(M.bond_energies(psi)), psi
def example_TEBD_gs_tf_ising_next_nearest_neighbor(L, g, Jp):
from tenpy.models.spins_nnn import SpinChainNNN2
from tenpy.models.model import NearestNeighborModel
print(
"finite TEBD, imaginary time evolution, transverse field Ising next-nearest neighbor"
)
print("L={L:d}, g={g:.2f}, Jp={Jp:.2f}".format(L=L, g=g, Jp=Jp))
model_params = dict(
L=L,
Jx=1.,
Jy=0.,
Jz=0.,
Jxp=Jp,
Jyp=0.,
Jzp=0.,
hz=g,
bc_MPS='finite',
conserve=None,
)
# we start with the non-grouped sites, but next-nearest neighbor interactions, building the MPO
M = SpinChainNNN2(model_params)
product_state = ["up"] * M.lat.N_sites
psi = MPS.from_product_state(M.lat.mps_sites(),
product_state,
bc=M.lat.bc_MPS)
# now we group each to sites ...
psi.group_sites(n=2) # ... in the state
M.group_sites(n=2) # ... and model
# now, M has only 'nearest-neighbor' interactions with respect to the grouped sites
# thus, we can convert the MPO into H_bond terms:
M_nn = NearestNeighborModel.from_MPOModel(
M) # hence, we can initialize H_bond from the MPO
# now, we continue to run TEBD as before
tebd_params = {
'order': 2,
'delta_tau_list': [0.1, 0.01, 0.001, 1.e-4, 1.e-5],
'N_steps': 10,
'max_error_E': 1.e-6,
'trunc_params': {
'chi_max': 30,
'svd_min': 1.e-10
},
}
eng = tebd.TEBDEngine(psi, M_nn, tebd_params) # use M_nn and grouped psi
eng.run_GS() # the main work...
# expectation values:
E = np.sum(M_nn.bond_energies(
psi)) # bond_energies() works only a for NearestNeighborModel
print("E = {E:.13f}".format(E=E))
print("final bond dimensions: ", psi.chi)
# we can split the sites of the state again for an easier evaluation of expectation values
psi.group_split()
mag_x = 2. * np.sum(
psi.expectation_value("Sx")) # factor of 2 for Sx vs Sigmax
mag_z = 2. * np.sum(psi.expectation_value("Sz"))
print("magnetization in X = {mag_x:.5f}".format(mag_x=mag_x))
print("magnetization in Z = {mag_z:.5f}".format(mag_z=mag_z))
return E, psi, M
def test_tebd(bc_MPS, g=0.5):
L = 2 if bc_MPS == 'infinite' else 6
# xxz_pars = dict(L=L, Jxx=1., Jz=3., hz=0., bc_MPS=bc_MPS)
# M = XXZChain(xxz_pars)
# factor of 4 (2) for J (h) to change spin-1/2 to Pauli matrices
model_pars = dict(L=L,
Jx=0.,
Jy=0.,
Jz=-4.,
hx=2. * g,
bc_MPS=bc_MPS,
conserve=None)
M = SpinChain(model_pars)
state = ([[1, -1.], [1, -1.]] * L)[:L] # pointing in (-x)-direction
psi = MPS.from_product_state(M.lat.mps_sites(), state, bc=bc_MPS)
tebd_param = {
'dt': 0.01,
'order': 2,
'delta_tau_list': [0.1, 1.e-4, 1.e-8],
'max_error_E': 1.e-9,
'trunc_params': {
'chi_max': 50,
'trunc_cut': 1.e-13
}
}
engine = tebd.TEBDEngine(psi, M, tebd_param)
engine.run_GS()
print("norm_test", psi.norm_test())
if bc_MPS == 'finite':
psi.canonical_form()
ED = ExactDiag(M)
ED.build_full_H_from_mpo()
ED.full_diagonalization()
E_ED, psi_ED = ED.groundstate()
Etebd = np.sum(M.bond_energies(psi))
print("E_TEBD={Etebd:.14f} vs E_exact={Eex:.14f}".format(Etebd=Etebd,
Eex=E_ED))
assert (abs((Etebd - E_ED) / E_ED) < 1.e-7)
ov = npc.inner(psi_ED, ED.mps_to_full(psi), 'range', do_conj=True)
print("compare with ED: overlap = ", abs(ov)**2)
assert (abs(abs(ov) - 1.) < 1.e-7)
# Test real time TEBD: should change on an eigenstate
Sold = np.average(psi.entanglement_entropy())
for i in range(3):
engine.run()
Enew = np.sum(M.bond_energies(psi))
Snew = np.average(psi.entanglement_entropy())
assert (abs(Enew - Etebd) < 1.e-8)
assert (abs(Sold - Snew) < 1.e-5
) # somehow we need larger tolerance here....
if bc_MPS == 'infinite':
Etebd = np.average(M.bond_energies(psi))
Eexact = e0_tranverse_ising(g)
print("E_TEBD={Etebd:.14f} vs E_exact={Eex:.14f}".format(Etebd=Etebd,
Eex=Eexact))
Sold = np.average(psi.entanglement_entropy())
for i in range(2):
engine.run()
Enew = np.average(M.bond_energies(psi))
Snew = np.average(psi.entanglement_entropy())
assert (abs(Etebd - Enew) < 1.e-7)
assert (abs(Sold - Snew) < 1.e-5
) # somehow we need larger tolerance here....