def example_TEBD_gs_infinite(g):
print("infinite TEBD, imaginary time evolution, g={g:.2f}".format(g=g))
model_params = dict(L=2,
J=1.,
g=g,
bc_MPS='infinite',
conserve=None,
verbose=0)
M = TFIChain(model_params)
psi = MPS.from_product_state(M.lat.mps_sites(), [0] * 2, bc='infinite')
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
},
'verbose': 1
}
eng = tebd.Engine(psi, M, tebd_params)
eng.run_GS() # the main work...
E = np.mean(psi.expectation_value(M.H_bond))
print("E = {E:.13f}".format(E=E))
print("final bond dimensions: ", psi.chi)
print("correlation length:", psi.correlation_length())
# compare to exact result
E_exact = tfi_exact.infinite_gs_energy(1., g)
print("Analytic result: E/L = {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, verbose=True):
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, 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-8,
'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...
E = np.sum(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 example_DMRG_tf_ising_infinite(g, verbose=True):
print("infinite DMRG, transverse field Ising model")
print("g={g:.2f}".format(g=g))
model_params = dict(L=2, J=1., g=g, bc_MPS='infinite', 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': True, # setting this to True helps to escape local minima
'trunc_params': {
'chi_max': 30,
'svd_min': 1.e-10
},
'max_E_err': 1.e-10,
'verbose': verbose,
}
# instead of
# info = dmrg.run(psi, M, dmrg_params)
# E = info['E']
# we can also use the a Engine directly:
eng = dmrg.EngineCombine(psi, M, dmrg_params)
E, psi = eng.run() # equivalent to dmrg.run() up to the return parameters.
print("E = {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 example_1site_DMRG_tf_ising_infinite(g):
print("single-site infinite DMRG, transverse field Ising model")
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)
dmrg_params = {
'mixer': True, # setting this to True is essential for the 1-site algorithm to work.
'trunc_params': {
'chi_max': 30,
'svd_min': 1.e-10
},
'max_E_err': 1.e-10,
'combine': True
}
eng = dmrg.SingleSiteDMRGEngine(psi, M, dmrg_params)
E, psi = eng.run() # equivalent to dmrg.run() up to the return parameters.
print("E = {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))
def example_DMRG_infinite(g):
print("infinite DMRG, g={g:.2f}".format(g=g))
model_params = dict(L=2,
J=1.,
g=g,
bc_MPS='infinite',
conserve=None,
verbose=0)
M = TFIChain(model_params)
psi = MPS.from_product_state(M.lat.mps_sites(), [0] * 2, bc='infinite')
dmrg_params = {
'mixer': True,
'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.mean(psi.expectation_value(M.H_bond))
print("E = {E:.13f}".format(E=E))
print("final bond dimensions: ", psi.chi)
print("correlation length:", psi.correlation_length())
# compare to exact result
E_exact = tfi_exact.infinite_gs_energy(1., g)
print("Analytic result: E/L = {E:.13f}".format(E=E_exact))
print("relative error: ", abs((E - E_exact) / E_exact))
return E, psi, M
def example_TEBD_gs_infinite(g):
print("infinite TEBD, imaginary time evolution, g={g:.2f}".format(g=g))
import a_mps
import b_model
M = b_model.TFIModel(L=2, J=1., g=g, bc='infinite')
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.mean(psi.bond_expectation_value(M.H_bonds))
print("dt = {dt:.5f}: E/L = {E:.13f}".format(dt=dt, E=E))
print("final bond dimensions: ", psi.get_chi())
print("correlation length:", psi.correlation_length())
# compare to exact result
E_exact = tfi_exact.infinite_gs_energy(1., g)
print("Analytic result: E/L = {E:.13f}".format(E=E_exact))
print("relative error: ", abs((E - E_exact) / E_exact))
return E, psi, M
def example_DMRG_infinite(g):
print("infinite DMRG, g={g:.2f}".format(g=g))
import a_mps
import b_model
M = b_model.TFIModel(L=2, J=1., g=g, bc='infinite')
psi = a_mps.init_FM_MPS(M.L, M.d, M.bc)
eng = SimpleDMRGEngine(psi, M, chi_max=20, eps=1.e-14)
for i in range(20):
eng.sweep()
E = np.mean(psi.bond_expectation_value(M.H_bonds))
print("sweep {i:2d}: E/L = {E:.13f}".format(i=i + 1, E=E))
print("final bond dimensions: ", psi.get_chi())
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/L = {E:.13f}".format(E=E_exact))
print("relative error: ", abs((E - E_exact) / E_exact))
return E, psi, M
