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_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_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