def get(a):
n = 10
# create a random spin chain
spins = ["S=1/2" for i in range(n)] # spin 1/2 heisenberg chain
# create first neighbor exchange
sc = spinchain.Spin_Chain(spins) # create the spin chain
#sc.itensor_version = "julia"
h = 0
for i in range(n - 1):
h = h + sc.Sx[i] * sc.Sx[i + 1]
h = h + sc.Sy[i] * sc.Sy[i + 1]
h = h + sc.Sz[i] * sc.Sz[i + 1]
sc.set_hamiltonian(h)
sc.kpmmaxm = 20 # KPM maxm
sc.maxm = 20 # KPM maxm
A, B = sc.Sz[1], sc.Sz[1]
es = np.linspace(-0.5, 6, 2000)
delta = 1e-2
#sc.kpm_extrapolate = False
e = sc.gs_energy()
sc.kpm_extrapolate = True
sc.kpm_extrapolate_factor = 2.0
t0 = time.time()
(x, y) = sc.get_distribution(X=h - e,
xs=es,
delta=delta,
A=A,
B=B,
a=a,
b=0.9)
t1 = time.time()
print(a, t1 - t0)
return (x, y)
def get():
sc = spinchain.Spin_Chain(spins) # create the spin chain
h = 0
for i in range(n-1):
h = h +sc.Sx[i]*sc.Sx[i+1]
h = h +sc.Sy[i]*sc.Sy[i+1]
h = h +sc.Sz[i]*sc.Sz[i+1]
sc.set_hamiltonian(h)
return sc
def get(n):
spins = ["S=1/2" for i in range(n)] # spin 1/2 heisenberg chain
sc = spinchain.Spin_Chain(spins) # create the spin chain
h = 0
for i in range(n - 1):
h = h + sc.Sx[i] * sc.Sx[i + 1]
h = h + sc.Sy[i] * sc.Sy[i + 1]
h = h + sc.Sz[i] * sc.Sz[i + 1]
sc.set_hamiltonian(h)
return sc
def getsc(iv):
# create first neighbor exchange
sc = spinchain.Spin_Chain(spins) # create the spin chain
def fj(i,j):
if abs(i-j)==1: return 1.0
else: return 0.0
sc.set_exchange(fj)
sc.itensor_version = iv
sc.get_gs()
return sc
def get_original_Haldanechain(L=__L__):
#original Heisenberg
spins = ["S=1" for i in range(L)] # S=1 chain
sc = spinchain.Spin_Chain(spins) # create spin chain object
h = 0 # initialize Hamiltonian
for i in range(len(spins) - 1):
h = h + sc.Sx[i] * sc.Sx[i + 1]
h = h + sc.Sy[i] * sc.Sy[i + 1]
h = h + sc.Sz[i] * sc.Sz[i + 1]
sc.set_hamiltonian(h)
return sc
def get(version, n=30):
spins = ["S=1/2" for i in range(n)] # spin 1/2 heisenberg chain
sc = spinchain.Spin_Chain(spins) # create the spin chain
if version == "julia": sc.setup_julia() # setup the Julia mode
h = 0
for i in range(n - 1):
h = h + sc.Sx[i] * sc.Sx[i + 1]
h = h + sc.Sy[i] * sc.Sy[i + 1]
h = h + sc.Sz[i] * sc.Sz[i + 1]
sc.set_hamiltonian(h)
return sc.gs_energy()
def get(version, n=30):
spins = ["S=1/2" for i in range(n)] # spin 1/2 heisenberg chain
sc = spinchain.Spin_Chain(spins) # create the spin chain
sc.itensor_version = version
h = 0
for i in range(n - 1):
h = h + sc.Sx[i] * sc.Sx[i + 1]
h = h + sc.Sy[i] * sc.Sy[i + 1]
h = h + sc.Sz[i] * sc.Sz[i + 1]
sc.set_hamiltonian(h)
return sc.gs_energy()
def get_energy(ind):
"""Given a certain ordering of the indexes, return the energy"""
n = len(ind)
spins = [2 for i in range(n)] # list with the different spins of your system
sc = spinchain.Spin_Chain(spins) # create the spin chain object
sc.maxm = 10 # bond dimension, controls the accuracy
sc.nsweeps = 3
def fj(i,j):
if abs(ind[i]-ind[j])==1: return 1.0
return 0.0
sc.set_exchange(fj) # add the exchange couplings
return sc.gs_energy()
def get_transformed_Haldanechain(L=__L__):
#transformed Heisenberg
spins = ["S=1" for i in range(L)] # S=1 chain
sc2 = spinchain.Spin_Chain(spins) # create spin chain object
h = 0 # initialize Hamiltonian
for i in range(len(spins) - 1):
expSx = -2 * sc2.Sx[i + 1] * sc2.Sx[i + 1] + mo.obj2MO(1)
expSz = -2 * sc2.Sz[i] * sc2.Sz[i] + mo.obj2MO(1)
h = h + sc2.Sx[i] * sc2.Sx[i + 1]
h = h + sc2.Sy[i] * expSz * expSx * sc2.Sy[i + 1]
h = h + sc2.Sz[i] * sc2.Sz[i + 1]
sc2.set_hamiltonian(h)
return sc2
def gets(b):
n = 30
spins = ["S=1/2" for i in range(n)] # spin 1/2 heisenberg chain
sc = spinchain.Spin_Chain(spins) # create the spin chain
h = 0
for i in range(n - 1):
h = h - sc.Sz[i] * sc.Sz[i + 1]
for i in range(n):
h = h - b * sc.Sx[i]
sc.set_hamiltonian(h)
wf = sc.get_gs() # compute ground state
return wf.get_entropy(n // 2)
def get_gap(bx):
"""
Compute the gap of the 1D Ising model with DMRG
"""
print("Computing B_x = ", bx)
sc = spinchain.Spin_Chain([2 for i in range(30)]) # create
h = 0
for i in range(sc.ns - 1):
h = h + sc.Sz[i] * sc.Sz[i + 1]
for i in range(sc.ns):
h = h + bx * sc.Sx[i]
sc.set_hamiltonian(h)
return abs(sc.vev(sc.Sz[0]))
es = sc.get_excited(mode="DMRG", n=2) # compute the first two energies
return es[1] - es[0] # return the gap
def getm(b):
n = 100 # number of sites in your chain
spins = ["S=1/2" for i in range(n)] # create the sites
sc = spinchain.Spin_Chain(spins) # create the chain
h = 0
for i in range(n-1):
h = h + sc.Sx[i]*sc.Sx[i+1] # add exchange
h = h + sc.Sy[i]*sc.Sy[i+1] # add exchange
h = h + sc.Sz[i]*sc.Sz[i+1] # add exchange
for i in range(n): h = h + b*sc.Sz[i] # add transverse field
Mz = 0
for i in range(n): Mz = Mz + sc.Sz[i]
sc.set_hamiltonian(h) # and initialize the Hamiltonian
mz = sc.vev(Mz,mode="DMRG").real
return mz
def get(c01):
"""Compute mutual information"""
# Heisenberg model
sc = spinchain.Spin_Chain(spins) # create the spin chain
h = 0
for i in range(n - 1):
c = 1.0 # default coupling
if i == 1: c = c01 # if it is the middle, change the coupling
h = h + c * sc.Sx[i] * sc.Sx[i + 1]
h = h + c * sc.Sy[i] * sc.Sy[i + 1]
h = h + c * sc.Sz[i] * sc.Sz[i + 1]
sc.set_hamiltonian(h)
wf = sc.get_gs() # compute ground state
s = wf.get_mutual_information(1, 2) # mutual information
print(c01, s)
return s
def get(n=2,bx=0.):
g = geometry.single_square_lattice()
m = g.get_supercell(n).get_hamiltonian(has_spin=False).get_hk_gen()([0.,0.,0.])
n = m.shape[0] # number of sites in your chain
spins = ["S=1/2" for i in range(n)] # create the sites
sc = spinchain.Spin_Chain(spins) # create the chain
h = 0
# now define the Hamiltonian
for i in range(n):
for j in range(n):
h = h + (-1)*m[i,j]*sc.Sz[i]*sc.Sz[j]
h = 4*h + 2*bx*sum(sc.Sx)
sc.set_hamiltonian(h)
es = sc.get_excited(n=2,mode="ED")
return es[1]-es[0]
def get(c01):
"""Compute entropy"""
# Heisenberg model
sc = spinchain.Spin_Chain(spins) # create the spin chain
h = 0
for i in range(n-1):
c = 1.0 # default coupling
if i==1: c = c01 # if it is the middle, change the coupling
h = h +c*sc.Sx[i]*sc.Sx[i+1]
h = h +c*sc.Sy[i]*sc.Sy[i+1]
h = h +c*sc.Sz[i]*sc.Sz[i+1]
sc.set_hamiltonian(h)
wf = sc.get_gs() # compute ground state
s = wf.get_pair_entropy(0,1) # entropy of the sites (0,1) with the rest
# Alternative method
# s1 = wf.get_bond_entropy(1,2) # compute entropy at this bond
# print(s,s1,s1/s)
return s
def run_classcal_precalculation(n_qubit, hamiltonian: QubitOperator, calc_2DM=False, get_amps=False):
spins = ["S=1/2" for i in range(n_qubit)]
sc = spinchain.Spin_Chain(spins)
dmrgpy_hamiltonian = QubitOperator2DmrgpyOperator(n_qubit, hamiltonian)
# print(dmrgpy_hamiltonian.op)
sc.set_hamiltonian(dmrgpy_hamiltonian)
gs_energy = sc.gs_energy(mode="ED")
ed_obj = sc.get_ED_obj()
res = {}
res["energy"] = gs_energy
if calc_2DM:
one_DM, two_DM = get_one_two_density_matrix(n_qubit, ed_obj)
res["2DM"] = two_DM
res["1DM"] = one_DM
entropy = [entropy_one_DM(one_DM[i]) for i in range(n_qubit)]
res["entropy"] = entropy
if get_amps:
res["amplitudes"]=ed_obj.get_gs()
return res
def get(D):
sc = spinchain.Spin_Chain(spins) # create the spin chain
h = 0
for i in range(len(spins) - 1):
h = h + sc.Sx[i] * sc.Sx[i + 1]
h = h + sc.Sy[i] * sc.Sy[i + 1]
h = h + sc.Sz[i] * sc.Sz[i + 1]
for i in range(len(spins)):
h = h - D * sc.Sz[i] * sc.Sz[i]
# define a Neel Hamiltonian
h0 = 0
for i in range(len(spins)):
h0 = h0 + ((-1)**i) * sc.Sz[i]
sc.nsweeps = 5
sc.maxm = 20
sc.set_hamiltonian(h0)
wf = sc.get_gs() # get the Neel wavefunction
sc.set_hamiltonian(h)
nc = len(spins) // 3
wf = sc.get_gs(wf0=wf)
print(D)
return wf.get_entropy(len(spins) // 2)
# Add the root path of the dmrgpy library import os import sys sys.path.append(os.getcwd() + '/../../src') import numpy as np from dmrgpy import spinchain n = 6 spins = [2 for i in range(n)] # spin 1/2 heisenberg chain sc = spinchain.Spin_Chain(spins) # create the spin chain e = sc.gs_energy() # compute the ground state energy # now get the low energy Hamiltonian h, b = sc.get_effective_hamiltonian() print(sc.get_excited(n=4)) import scipy.linalg as lg print(np.round(lg.eigvalsh(b), 3)) es, vs = lg.eigh(-b) vs = vs.transpose() print(vs[0].real) print(np.round(lg.eigvalsh(h), 3))
if i == j: return -2 * U # set to half filling
return 0.0
def fu(i, j):
if i == j: return U
return 0.0
fc.set_hoppings(ft) # add the term to the Hamiltonian
fc.set_hubbard(fu) # add the term to the Hamiltonian
pairs = [(0, i) for i in range(n)]
ch = fc.get_correlator(pairs=pairs, name="YY", mode="DMRG").real
print(fc.get_density_spinful())
# now create the Heisenberg chain
sc = spinchain.Spin_Chain([2 for i in range(n)])
sc.set_exchange(lambda i, j: 1.0 * (abs(i - j) == 1))
cs = sc.get_correlator(pairs=pairs, name="XX", mode="DMRG").real
import matplotlib.pyplot as plt
inds = range(len(ch))
plt.scatter(inds, ch, c="red", label="Hubbard")
plt.plot(inds, cs, c="blue", label="Heisenberg")
#plt.plot(inds,mz2,c="green",label="Exact")
plt.legend()
plt.xlabel("Site")
plt.ylabel("Correlator")
plt.show()
# Add the root path of the dmrgpy library
import os
import sys
sys.path.append(os.getcwd() + '/../../src')
import numpy as np # conventional numpy library
import matplotlib.pyplot as plt # library to plot the results
from dmrgpy import spinchain
ns = 6 # number of sites in the spin chain
spins = [3 for i in range(ns)] # S=1 chain
sc = spinchain.Spin_Chain(spins) # create spin chain object
# now define a custom Hamiltonian
h = 0.0 # initialize Hamiltonian
Si = [sc.Sx, sc.Sy, sc.Sz] # store the three components
for i in range(ns - 1): # loop
for S in Si:
h = h + S[i] * S[i + 1] # bilinear
for S in Si:
h = h + 1. / 3. * S[i] * S[i + 1] * S[i] * S[i + 1] # biquadratic
sc.set_hamiltonian(h) # create the Hamiltonian
print("Energy with DMRG", sc.gs_energy(mode="DMRG"))
print("Energy with ED", sc.gs_energy(mode="ED"))