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 example_DMRG_heisenberg_xxz_infinite(Jx=1,
Jy=1,
Jz=1,
hx=0,
hy=0,
hz=0,
conserve='best',
verbose=False,
chi_max=100,
S=0.5):
if verbose:
print("infinite DMRG, Heisenberg XXZ chain")
print("Jz={Jz:.2f}, conserve={conserve!r}".format(
Jz=Jz, conserve=conserve))
model_params = dict(
L=2,
S=S, # spin 1/2
Jx=Jx,
Jy=Jy,
Jz=Jz, # couplings
hx=hx,
hy=hy,
hz=hz,
bc_MPS='infinite',
conserve=conserve,
verbose=verbose)
M = SpinModel(model_params)
product_state = ["up", "up"] # initial Neel state
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': chi_max,
'svd_min': 1.e-10,
},
'max_E_err': 1.e-10,
'verbose': verbose,
}
info = dmrg.run(psi, M, dmrg_params)
E = info['E']
if verbose:
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)
if verbose:
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!
if verbose:
print("correlation length:", psi.correlation_length())
corrs = psi.correlation_function("Sz", "Sz", sites1=range(10))
if verbose:
print("correlations <Sz_i Sz_j> =")
print(corrs)
return E, psi, M
"""Initialization of the Heisenberg model on a kagome lattice."""
# Copyright 2019 TeNPy Developers, GNU GPLv3
from tenpy.models.spins import SpinModel
model_params = {
"S": 0.5, # Spin 1/2
"lattice": "Kagome",
"bc_MPS": "infinite",
"bc_y": "cylinder",
"Ly": 2, # defines cylinder circumference
"conserve": "Sz", # use Sz conservation
"Jx": 1.,
"Jy": 1.,
"Jz": 1. # Heisenberg coupling
}
model = SpinModel(model_params)