def calc_infinite_groundstates(dmrg_params, g=0.1):
L = 2
model_params = dict(L=L,
J=1.,
g=g,
bc_MPS='infinite',
conserve=None,
verbose=0)
model = TFIChain(model_params)
plus_x = np.array([1., 1.]) / np.sqrt(2)
minus_x = np.array([1., -1.]) / np.sqrt(2)
psi_plus = MPS.from_product_state(model.lat.mps_sites(), [plus_x] * L,
model.lat.bc_MPS)
psi_minus = MPS.from_product_state(model.lat.mps_sites(), [minus_x] * L,
model.lat.bc_MPS)
engine_plus = dmrg.TwoSiteDMRGEngine(psi_plus, model, dmrg_params)
engine_plus.run()
print("<Sx> =", psi_plus.expectation_value("Sigmax"))
engine_minus = dmrg.TwoSiteDMRGEngine(psi_minus, model, dmrg_params)
engine_minus.run()
print("<Sx> =", psi_minus.expectation_value("Sigmax"))
data_plus = {'psi': psi_plus}
data_plus.update(**engine_plus.env.get_initialization_data())
data_minus = {'psi': psi_minus}
data_minus.update(**engine_minus.env.get_initialization_data())
return model, data_plus, data_minus
def example_DMRG_heisenberg_xxz_finite(L, Jz, chi, conserve='best', verbose=True):
print("finite DMRG, Heisenberg XXZ chain")
print("L={L:d}, Jz={Jz:.2f}".format(L=L, Jz=Jz))
model_params = dict(L=L, S=0.5, Jx=1., Jy=1., Jz=Jz,
bc_MPS='finite', conserve=conserve, verbose=verbose)
M = SpinModel(model_params)
product_state = ["up", "down"] * (M.lat.N_sites // 2)
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
'max_E_err': 1.e-16,
'trunc_params': {
'chi_max': chi,
'svd_min': 1.e-16
},
'verbose': verbose,
}
info = dmrg.run(psi, M, dmrg_params) # the main work...
E = info['E']
E = E * 4
print("E = {E:.13f}".format(E=E))
print("final bond dimensions: ", psi.chi)
Sz = psi.expectation_value("Sz") # Sz instead of Sigma z: spin-1/2 operators!
mag_z = np.mean(Sz)
print("<S_z> = [{Sz0:.5f}, {Sz1:.5f}]; mean ={mag_z:.5f}".format(Sz0=Sz[0],
Sz1=Sz[1],
mag_z=mag_z))
# note: it's clear that mean(<Sz>) is 0: the model has Sz conservation!
corrs = psi.correlation_function("Sz", "Sz", sites1=range(10))
print("correlations <Sz_i Sz_j> =")
print(corrs)
return E, psi, M
def run_tebd_tfi(L, mindim, g, tf, dt, verbose=False, order=2):
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': order,
'dt': dt,
'N_steps': int(tf / dt),
'trunc_params': {
'trunc_cut': 1e-14,
'svd_min': 1e-24,
'chi_max': mindim
# 'chi_min': mindim
},
'verbose': verbose,
}
eng = tebd.Engine(psi, M, tebd_params)
eng.run()
print(np.amax(psi.chi))
return psi
def DMRG_tf_ising_finite(Lx, Ly, g, verbose=True):
print("finite DMRG, transverse field Ising model")
print("Lx={Lx:d}, Ly={Ly:d}, g={g:.2f}".format(Lx=Lx, Ly=Ly, g=g))
M = TFIModel(
dict(g=g,
J=1.,
lattice='Triangular',
bc_MPS='finite',
Lx=Lx,
Ly=Ly,
conserve=None,
verbose=verbose))
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,
'max_E_err': 1.e-10,
'trunc_params': {
'chi_max': 30,
'svd_min': 1.e-10
},
'verbose': verbose,
'combine': True
}
info = dmrg.run(psi, M, dmrg_params)
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))
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 test_ToricCode(Lx=1, Ly=2):
with warnings.catch_warnings():
warnings.simplefilter('ignore')
model_params = {'Lx': Lx, 'Ly': Ly}
M = ToricCode(model_params)
psi = MPS.from_product_state(M.lat.mps_sites(), [0] * M.lat.N_sites,
bc='infinite')
dmrg_params = {
'mixer': True,
'trunc_params': {
'chi_max': 10,
'svd_min': 1.e-10
},
'max_E_err': 1.e-10,
'N_sweeps_check': 4,
'verbose': 1
}
result = dmrg.run(psi, M, dmrg_params)
E = result['E']
print("E =", E)
psi.canonical_form()
# energy per "cell"=2 -> energy per site in the dual lattice = 1
assert abs(E - (-1.)) < dmrg_params['max_E_err']
print("chi=", psi.chi)
if Ly == 2:
assert tuple(psi.chi[:4]) == (2, 4, 4, 4)
assert abs(
psi.entanglement_entropy(bonds=[0])[0] - np.log(2) *
(Ly - 1)) < 1.e-5
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 test_tebd(bc_MPS, g=0.5):
L = 2 if bc_MPS == 'infinite' else 6
# xxz_pars = dict(L=L, Jxx=1., Jz=3., hz=0., bc_MPS=bc_MPS)
# M = XXZChain(xxz_pars)
# factor of 4 (2) for J (h) to change spin-1/2 to Pauli matrices
model_pars = dict(L=L, Jx=0., Jy=0., Jz=-4., hx=2. * g, bc_MPS=bc_MPS, conserve=None)
M = SpinChain(model_pars)
state = ([[1, -1.], [1, -1.]] * L)[:L] # pointing in (-x)-direction
psi = MPS.from_product_state(M.lat.mps_sites(), state, bc=bc_MPS)
tebd_param = {
'verbose': 2,
'dt': 0.01,
'order': 2,
'delta_tau_list': [0.1, 1.e-4, 1.e-8],
'max_error_E': 1.e-9,
'trunc_params': {
'chi_max': 50,
'trunc_cut': 1.e-13
}
}
engine = tebd.Engine(psi, M, tebd_param)
engine.run_GS()
print("norm_test", psi.norm_test())
if bc_MPS == 'finite':
psi.canonical_form()
ED = ExactDiag(M)
ED.build_full_H_from_mpo()
ED.full_diagonalization()
psi_ED = ED.groundstate()
Etebd = np.sum(M.bond_energies(psi))
Eexact = np.min(ED.E)
print("E_TEBD={Etebd:.14f} vs E_exact={Eex:.14f}".format(Etebd=Etebd, Eex=Eexact))
assert (abs((Etebd - Eexact) / Eexact) < 1.e-7)
ov = npc.inner(psi_ED, ED.mps_to_full(psi), do_conj=True)
print("compare with ED: overlap = ", abs(ov)**2)
assert (abs(abs(ov) - 1.) < 1.e-7)
# Test real time TEBD: should change on an eigenstate
Sold = np.average(psi.entanglement_entropy())
for i in range(3):
engine.run()
Enew = np.sum(M.bond_energies(psi))
Snew = np.average(psi.entanglement_entropy())
assert (abs(Enew - Etebd) < 1.e-8)
assert (abs(Sold - Snew) < 1.e-5) # somehow we need larger tolerance here....
if bc_MPS == 'infinite':
Etebd = np.average(M.bond_energies(psi))
Eexact = e0_tranverse_ising(g)
print("E_TEBD={Etebd:.14f} vs E_exact={Eex:.14f}".format(Etebd=Etebd, Eex=Eexact))
Sold = np.average(psi.entanglement_entropy())
for i in range(2):
engine.run()
Enew = np.average(M.bond_energies(psi))
Snew = np.average(psi.entanglement_entropy())
assert (abs(Etebd - Enew) < 1.e-7)
assert (abs(Sold - Snew) < 1.e-5) # somehow we need larger tolerance here....
def run_tenpy_tdvp(L, maxdim, tf, verbose=False):
model_params = dict(L=L,
J=1.,
g=1,
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)
tdvp_params = {
'start_time': 0,
'dt': 0.1,
'trunc_params': {
'chi_max': maxdim,
'svd_min': 0,
'trunc_cut': None
}
}
tdvp_engine = tdvp.Engine(psi=psi, model=M, TDVP_params=tdvp_params)
tdvp_engine.run_two_sites(N_steps=int(tf / 0.1))
return np.amax(psi.chi)
def example_DMRG_tf_ising_finite(L, g, h=0, chi=2, verbose=True):
print("finite DMRG, transverse field Ising model")
print("L={L:d}, g={g:.2f}, h={h:.2f}".format(L=L, g=g, h=h))
model_params = dict(L=L, J=1., g=g, bc_MPS='finite', h=h)
M = IsingChain(model_params)
# 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-16,
'trunc_params': {
'chi_max': chi,
'svd_min': 1.e-16
},
'verbose': verbose,
}
info = dmrg.run(psi, M, dmrg_params) # the main work...
E = info['E']
print("E = {E:.16f}".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))
return E, psi, M
def run_out_of_equilibrium():
L = 10
chi = 5
delta_t = 0.1
model_params = {
'L': L,
'S': 0.5,
'conserve': 'Sz',
'Jz': 1.0,
'Jy': 1.0,
'Jx': 1.0,
'hx': 0.0,
'hy': 0.0,
'hz': 0.0,
'muJ': 0.0,
'bc_MPS': 'finite',
}
heisenberg = tenpy.models.spins.SpinChain(model_params)
product_state = ["up"] * int(L / 2) + ["down"] * (
L - int(L / 2)
) #starting from a product state which is not an eigenstate of the Heisenberg model
psi = MPS.from_product_state(heisenberg.lat.mps_sites(),
product_state,
bc=heisenberg.lat.bc_MPS,
form='B')
tdvp_params = {
'start_time': 0,
'dt': delta_t,
'trunc_params': {
'chi_max': chi,
'svd_min': 1.e-10,
'trunc_cut': None
}
}
tdvp_engine = tdvp.Engine(psi=psi,
model=heisenberg,
TDVP_params=tdvp_params)
times = []
S_mid = []
for i in range(30):
tdvp_engine.run_two_sites(N_steps=1)
times.append(tdvp_engine.evolved_time)
S_mid.append(psi.entanglement_entropy(bonds=[L // 2])[0])
for i in range(30):
tdvp_engine.run_one_site(N_steps=1)
#psi_2=copy.deepcopy(psi)
#psi_2.canonical_form()
times.append(tdvp_engine.evolved_time)
S_mid.append(psi.entanglement_entropy(bonds=[L // 2])[0])
import matplotlib.pyplot as plt
plt.figure()
plt.plot(times, S_mid)
plt.xlabel('t')
plt.ylabel('S')
plt.axvline(x=3.1, color='red')
plt.text(0.0, 0.0000015, "Two sites update")
plt.text(3.1, 0.0000015, "One site update")
plt.show()
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 __init__(self, L=10, Jn=1, Jnn=0, hz=0, options={}):
# use predefined local Hilbert space and onsite operators
site = SpinSite(S=1 / 2, conserve=None)
self.L = L
lat = Chain(L, site, bc="open", bc_MPS="finite") # define geometry
MultiCouplingModel.__init__(self, lat)
# add terms of the Hamiltonian;
# operators "Sx", "Sy", "Sz" are defined by the SpinSite
self.add_coupling(Jn, 0, "Sx", 0, "Sx", 1)
self.add_coupling(Jn, 0, "Sy", 0, "Sy", 1)
self.add_coupling(Jn, 0, "Sz", 0, "Sz", 1)
self.add_multi_coupling(
Jnn, [("Sx", -1, 0), ("Sx", 1, 0)]
) #(oper, shift, internal index - it's possible to merge sites together)
self.add_multi_coupling(Jnn, [("Sy", -1, 0), ("Sy", 1, 0)])
self.add_multi_coupling(Jnn, [("Sz", -1, 0), ("Sz", 1, 0)])
self.add_onsite(hz, 0, "Sz")
# finish initialization
MPOModel.__init__(self, lat, self.calc_H_MPO())
self.psi = MPS.from_product_state(self.lat.mps_sites(), [0] * L,
"finite")
self.options = options
self.dmrg_retval = None
def test_ExpMPOEvolution(bc_MPS, approximation, compression, g=1.5):
# Test a time evolution against exact diagonalization for finite bc
dt = 0.01
if bc_MPS == 'finite':
L = 6
else:
L = 2
model_pars = dict(L=L,
Jx=0.,
Jy=0.,
Jz=-4.,
hx=2. * g,
bc_MPS=bc_MPS,
conserve=None)
M = SpinChain(model_pars)
state = ([[1 / np.sqrt(2), -1 / np.sqrt(2)]] * L
) # pointing in (-x)-direction
state = ['up'] * L # pointing in (-z)-direction
psi = MPS.from_product_state(M.lat.mps_sites(), state, bc=bc_MPS)
options = {
'dt': dt,
'N_steps': 1,
'order': 1,
'approximation': approximation,
'compression_method': compression,
'trunc_params': {
'chi_max': 30
}
}
eng = mpo_evolution.ExpMPOEvolution(psi, M, options)
if bc_MPS == 'finite':
ED = exact_diag.ExactDiag(M)
ED.build_full_H_from_mpo()
ED.full_diagonalization()
psiED = ED.mps_to_full(psi)
psiED /= psiED.norm()
UED = ED.exp_H(dt)
for i in range(30):
psi = eng.run()
psiED = npc.tensordot(UED, psiED, ('ps*', [0]))
psi_full = ED.mps_to_full(psi)
assert (abs(abs(npc.inner(psiED, psi_full, [0, 0], True)) - 1) <
dt)
if bc_MPS == 'infinite':
psiTEBD = psi.copy()
TEBD_params = {'dt': dt, 'N_steps': 1}
EngTEBD = tebd.Engine(psiTEBD, M, TEBD_params)
for i in range(30):
EngTEBD.run()
psi = eng.run()
print(psi.norm)
print(np.abs(psi.overlap(psiTEBD) - 1))
#This test fails
assert (abs(abs(psi.overlap(psiTEBD)) - 1) < 1e-2)
def main():
L = 60
chi = 80
U = 10.0
beta = 0.02
file_name = "U" + str(int(U)) +\
"_L"+str(L)+\
"_Ds_ch"+str(chi)+\
".pkl"
verbose_model = 0
verbose_dmrg = 0
t = 1.0
Mu = 16.0
alpha = 0.5
cnsrv_bsn = 'N'
cnsrv_spn = None
pkl_pack = []
for ddelta in range(51):
delta = 0.50 + ddelta * 0.01
model_params = {
'n_max': 2,
'L': L,
'bc_MPS': 'finite',
'filling': 0.5,
't': t,
'U': U,
'mu': Mu,
'alpha': alpha,
'delta': delta,
'beta': beta,
'conserve_boson': cnsrv_bsn,
'conserve_spin': cnsrv_spn,
'verbose': verbose_model
}
M = BosonSpin(model_params)
initial_state = [0] * (L // 2) + [2] * (L // 2)
psi = MPS.from_product_state(M.lat.mps_sites(),
initial_state,
bc='finite')
dmrg_params = {'mixer': None, 'verbose': verbose_dmrg, \
'trunc_params': {'chi_max': chi, 'svd_min': 1.e-10}}
start_time = time.time()
dmrg.run(psi, M, dmrg_params)
end_time = time.time()
print("$\Delta = {a:.04f}$\tDMRG time = {b}".format(a=delta,
b=end_time -
start_time))
pkl_pack += [[psi, model_params, dmrg_params]]
with open(file_name, 'wb') as g:
pickle.dump(pkl_pack, g)
return 0
def main():
L = 80
delta = 0.9064
file_name="L"+str(L) + \
"_D"+str(int(delta*10000))+\
"E0" + \
"_CHIall.pkl"
verbose_model = 0
verbose_dmrg = 0
t = 1.0
alpha = 0.5
beta = 0.02
cnsrv_bsn = 'Sz'
cnsrv_spn = None
model_params = {
'L': L,
'bc_MPS': 'finite',
't': t,
'alpha': alpha,
'delta': delta,
'beta': beta,
'conserve_fermionic_boson': cnsrv_bsn,
'conserve_spin': cnsrv_spn,
'verbose': verbose_model
}
M = FermionOnSpinLattice(model_params)
initial_state = [0] * (L // 2) + [2] * (L // 2)
pkl_pack = [model_params, M]
chi_start = np.arange(10) + 5
chi_end = np.arange(35) * 2 + 15
#chis = np.concatenate((chi_start, chi_end))
# extra chi for 80
chis = np.arange(10) * 2 + 85
for chi in chis:
psi = MPS.from_product_state(M.lat.mps_sites(),
initial_state,
bc='finite')
dmrg_params = {'mixer': None, 'verbose': verbose_dmrg, \
'trunc_params': {'chi_max': chi, 'svd_min': 1.e-10}}
start_time = time.time()
dmrg.run(psi, M, dmrg_params)
end_time = time.time()
print("D max = {c}\tDMRG time = {b}".format(c=chi,
b=end_time - start_time))
pkl_pack += [[psi, chi]]
with open(file_name, 'wb') as g:
pickle.dump(pkl_pack, g)
return 0
def run(phi_ext=np.linspace(0, 1.0, 11)):
data = dict(phi_ext=phi_ext, QL=[], ent_spectrum=[])
model_params = dict(conserve='N',
filling=1 / 2.,
Lx=1,
Ly=3,
t=-1.,
mu=0,
V=1.,
phi_ext=0.,
bc_MPS='infinite',
bc_y='cylinder',
verbose=0)
dmrg_params = {
'mixer': True, # setting this to True helps to escape local minima
'mixer_params': {
'amplitude': 1.e-5,
'decay': 1.2,
'disable_after': 30
},
'trunc_params': {
'svd_min': 1.e-10,
},
'lanczos_params': {
'N_min': 5,
'N_max': 20
},
'chi_list': {
0: 9,
10: 49,
20: 200
},
'max_E_err': 1.e-10,
'max_S_err': 1.e-6,
'max_sweeps': 150,
'verbose': 1.,
}
prod_state = ['full', 'empty'] * (model_params['Lx'] * model_params['Ly'] * 2 // 2)
# TODO allow tiling of list in from_product_state...
eng = None
for phi in phi_ext:
print("=" * 100)
print("phi_ext = ", phi)
model_params['phi_ext'] = phi
if eng is None: # first time in the loop
M = FermionicHaldaneModel(model_params)
psi = MPS.from_product_state(M.lat.mps_sites(), prod_state, bc=M.lat.bc_MPS)
eng = dmrg.EngineCombine(psi, M, dmrg_params)
else:
del eng.DMRG_params['chi_list']
M = FermionicHaldaneModel(model_params)
eng.init_env(model=M)
E, psi = eng.run()
data['QL'].append(psi.average_charge(bond=0)[0])
data['ent_spectrum'].append(psi.entanglement_spectrum(by_charge=True)[0])
return data
