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_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_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_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
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
