def example_DMRG_tf_ising_finite(L, g, verbose=True):
print("finite DMRG, transverse field Ising model")
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, verbose=verbose)
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)
dmrg_params = {
'mixer': None, # setting this to True helps to escape local minima
'max_E_err': 1.e-10,
'trunc_params': {
'chi_max': 30,
'svd_min': 1.e-10
},
'verbose': verbose,
}
info = dmrg.run(psi, M, dmrg_params) # the main work...
E = info['E']
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_finite(L, g):
print("finite TEBD, imaginary time evolution, 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,
verbose=0)
M = TFIChain(model_params)
psi = MPS.from_product_state(M.lat.mps_sites(), [0] * L, bc='finite')
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
},
'verbose': 1
}
eng = tebd.Engine(psi, M, tebd_params)
eng.run_GS() # the main work...
E = np.sum(psi.expectation_value(M.H_bond[1:]))
print("E = {E:.13f}".format(E=E))
print("final bond dimensions: ", psi.chi)
if L < 20: # compare to exact result
E_exact = tfi_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_DMRG_finite(L, g):
print("finite DMRG, 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,
verbose=0)
M = TFIChain(model_params)
psi = MPS.from_product_state(M.lat.mps_sites(), [0] * L, bc='finite')
dmrg_params = {
'mixer': None,
'trunc_params': {
'chi_max': 30,
'svd_min': 1.e-10
},
'max_E_err': 1.e-10,
'verbose': 1
}
dmrg.run(psi, M, dmrg_params)
E = np.sum(psi.expectation_value(M.H_bond[1:]))
print("E = {E:.13f}".format(E=E))
print("final bond dimensions: ", psi.chi)
if L < 20: # compare to exact result
E_exact = tfi_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_finite(L, J, g):
print("finite TEBD, (imaginary time evolution)")
print("L={L:d}, J={J:.1f}, g={g:.2f}".format(L=L, J=J, g=g))
import a_mps
import b_model
model = b_model.TFIModel(L, J=J, g=g)
psi = a_mps.init_spinup_MPS(L)
for dt in [0.1, 0.01, 0.001, 1.e-4, 1.e-5]:
U_bonds = calc_U_bonds(model, dt)
run_TEBD(psi, U_bonds, N_steps=500, chi_max=30, eps=1.e-10)
E = model.energy(psi)
print("dt = {dt:.5f}: E = {E:.13f}".format(dt=dt, E=E))
print("final bond dimensions: ", psi.get_chi())
if L < 20: # for small systems compare to exact diagonalization
E_exact = tfi_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, model
def example_DMRG_finite(L, g):
print("finite DMRG, L={L:d}, g={g:.2f}".format(L=L, g=g))
import a_mps
import b_model
M = b_model.TFIModel(L=L, J=1., g=g, bc='finite')
psi = a_mps.init_FM_MPS(M.L, M.d, M.bc)
eng = SimpleDMRGEngine(psi, M, chi_max=30, eps=1.e-10)
for i in range(10):
eng.sweep()
E = np.sum(psi.bond_expectation_value(M.H_bonds))
print("sweep {i:2d}: E = {E:.13f}".format(i=i + 1, E=E))
print("final bond dimensions: ", psi.get_chi())
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_finite(L, g):
print("finite TEBD, imaginary time evolution, L={L:d}, g={g:.2f}".format(
L=L, g=g))
import a_mps
import b_model
M = b_model.TFIModel(L, J=1., g=g)
psi = a_mps.init_FM_MPS(M.L, M.d, M.bc)
for dt in [0.1, 0.01, 0.001, 1.e-4, 1.e-5]:
U_bonds = calc_U_bonds(M.H_bonds, dt)
run_TEBD(psi, U_bonds, N_steps=500, chi_max=30, eps=1.e-10)
E = np.sum(psi.bond_expectation_value(M.H_bonds))
print("dt = {dt:.5f}: E = {E:.13f}".format(dt=dt, E=E))
print("final bond dimensions: ", psi.get_chi())
if L < 20: # compare to exact result
E_exact = tfi_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_finite(L, g, verbose=True):
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,
verbose=verbose)
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
},
'verbose': verbose,
}
eng = tebd.Engine(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_finite(L, g):
print("finite TEBD, imaginary time evolution, transverse field Ising")
print("L={L:d}, g={g:.2f}".format(L=L, g=g))
import a_mps
import b_model
M = b_model.TFIModel(L=L, J=1., g=g, bc='finite')
psi = a_mps.init_FM_MPS(M.L, M.d, M.bc)
for dt in [0.1, 0.01, 0.001, 1.e-4, 1.e-5]:
U_bonds = calc_U_bonds(M.H_bonds, dt)
run_TEBD(psi, U_bonds, N_steps=500, chi_max=30, eps=1.e-10)
E = np.sum(psi.bond_expectation_value(M.H_bonds))
print("dt = {dt:.5f}: E = {E:.13f}".format(dt=dt, E=E))
print("final bond dimensions: ", psi.get_chi())
mag_x = np.sum(psi.site_expectation_value(M.sigmax))
mag_z = np.sum(psi.site_expectation_value(M.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
