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