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ed_sz_nonconserved_no_kron_1d_heisenberg_J1J2_chain_spin_corr.py
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ed_sz_nonconserved_no_kron_1d_heisenberg_J1J2_chain_spin_corr.py
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#!/usr/bin/env python
# coding:utf-8
from __future__ import print_function
import math
import numpy as np
#import scipy.linalg
import scipy.sparse
import scipy.sparse.linalg
import argparse
import time
def parse_args():
parser = argparse.ArgumentParser(description='Calculate the ground state of S=1/2 Heisenberg chain')
parser.add_argument('-N', metavar='N',dest='N', type=int, default=8, help='set Nsize (should be >=4)')
parser.add_argument('-J1', metavar='J1',dest='J1', type=float, default=1.0, help='set J1')
parser.add_argument('-J2', metavar='J2',dest='J2', type=float, default=0.0, help='set J2')
return parser.parse_args()
def make_hamiltonian(Jxx,Jzz,list_isite1,list_isite2,N,Nint,Nhilbert):
listki = np.zeros((Nint+1)*Nhilbert,dtype=int)
loc = np.zeros((Nint+1)*Nhilbert,dtype=int)
elemnt = np.zeros((Nint+1)*Nhilbert,dtype=float)
listki = [i for k in range(Nint+1) for i in range(Nhilbert)]
for k in range(Nint): # loop for all interactions
isite1 = list_isite1[k]
isite2 = list_isite2[k]
is1 = 1<<isite1
is2 = 1<<isite2
is12 = is1 + is2
wght = 2.0*Jxx[k]
diag = Jzz[k]
for i in range(Nhilbert): # loop for all spin configurations
ibit = i & is12
loc[Nint*Nhilbert+i] = i # store diag index
if (ibit==0 or ibit==is12): # if (spin1,spin2) = (00) or (11)
elemnt[Nint*Nhilbert+i] += diag # store +Jzz
# print("# diag k(interactions) i(Hilbert)",k,i)
# print("# diag i ",np.binary_repr(i,width=N))
# print("# diag is12",np.binary_repr(is12,width=N))
# print("# diag ibit",np.binary_repr(ibit,width=N))
else: # if (spin1,spin2) = (01) or (10)
elemnt[Nint*Nhilbert+i] -= diag # store -Jzz
iexchg = i ^ is12
elemnt[k*Nhilbert+i] = wght # store 2*Jxx
loc[k*Nhilbert+i] = iexchg # store offdiag index
# print("# offdiag k(interactions) i(Hilbert)",k,i)
# print("# offdiag i ",np.binary_repr(i,width=N))
# print("# offdiag is12",np.binary_repr(is12,width=N))
# print("# offdiag iexc",np.binary_repr(iexchg,width=N))
HamCSR = scipy.sparse.csr_matrix((elemnt,(listki,loc)),shape=(Nhilbert,Nhilbert))
return HamCSR
def calc_zcorr(Nhilbert,Ncorr,list_corr_isite1,list_corr_isite2,psi):
szz = np.zeros(Ncorr,dtype=float)
for k in range(Ncorr): # loop for all bonds for correlations
isite1 = list_corr_isite1[k]
isite2 = list_corr_isite2[k]
is1 = 1<<isite1
is2 = 1<<isite2
is12 = is1 + is2
corr = 0.0
for i in range(Nhilbert): # loop for all spin configurations
ibit = i & is12
if (ibit==0 or ibit==is12): # if (spin1,spin2) = (00) or (11): factor = +1
factor = +1.0
else: # if (spin1,spin2) = (01) or (10): factor = -1
factor = -1.0
corr += factor*np.abs(psi[i])**2
szz[k] = 0.25 * corr
if (isite1==isite2):
szz[k] = 0.25
return szz
def calc_xcorr(Nhilbert,Ncorr,list_corr_isite1,list_corr_isite2,psi):
sxx = np.zeros(Ncorr,dtype=float)
for k in range(Ncorr): # loop for all bonds for correlations
isite1 = list_corr_isite1[k]
isite2 = list_corr_isite2[k]
is1 = 1<<isite1
is2 = 1<<isite2
is12 = is1 + is2
corr = 0.0
for i in range(Nhilbert): # loop for all spin configurations
ibit = i & is12
if (ibit==is1 or ibit==is2): # if (spin1,spin2) = (10) or (01)
iexchg = i ^ is12
corr += np.real(np.conj(psi[iexchg])*psi[i])
sxx[k] = 0.25 * corr
if (isite1==isite2):
sxx[k] = 0.25
return sxx
def make_lattice(N,J1,J2):
Jxx = []
Jzz = []
list_isite1 = []
list_isite2 = []
Nint = 0
for i in range(N):
site1 = i
site2 = (i+1)%N
site3 = (i+2)%N
#
list_isite1.append(site1)
list_isite2.append(site2)
Jxx.append(J1)
Jzz.append(J1)
Nint += 1
#
list_isite1.append(site1)
list_isite2.append(site3)
Jxx.append(J2)
Jzz.append(J2)
Nint += 1
return Jxx, Jzz, list_isite1, list_isite2, Nint
def main():
args = parse_args()
N = args.N
J1 = args.J1
J2 = args.J2
Nhilbert = 2**N
print("J1=",J1)
print("J2=",J2)
print("N=",N)
print("Nhilbert=",Nhilbert)
print("")
Jxx, Jzz, list_isite1, list_isite2, Nint = make_lattice(N,J1,J2)
print (Jxx)
print (Jzz)
print (list_isite1)
print (list_isite2)
print("Nint=",Nint)
start = time.time()
HamCSR = make_hamiltonian(Jxx,Jzz,list_isite1,list_isite2,N,Nint,Nhilbert)
end = time.time()
print (end - start)
# print (HamCSR)
start = time.time()
# ene,vec = scipy.sparse.linalg.eigsh(HamCSR,k=5)
ene,vec = scipy.sparse.linalg.eigsh(HamCSR,which='SA',k=5)
end = time.time()
print (end - start)
# print ("# GS energy:",ene[0])
print ("# energy:",ene[0],ene[1],ene[2],ene[3],ene[4])
# vec_sgn = np.sign(np.amax(vec[:,0]))
# print ("# GS wave function:")
# for i in range(Nhilbert):
# bini = np.binary_repr(i,width=N)
# print (i,vec[i,0]*vec_sgn,bini)
#
print("")
Ncorr = N # number of total correlations
list_corr_isite1 = [0 for k in range(Ncorr)] # site 1
list_corr_isite2 = [k for k in range(Ncorr)] # site 2
print (list_corr_isite1)
print (list_corr_isite2)
psi = vec[:,0] # choose the ground state
start = time.time()
szz = calc_zcorr(Nhilbert,Ncorr,list_corr_isite1,list_corr_isite2,psi)
sxx = calc_xcorr(Nhilbert,Ncorr,list_corr_isite1,list_corr_isite2,psi)
ss = szz+sxx+sxx
stot2 = N*np.sum(ss)
end = time.time()
print (end - start)
print ("# szz:",szz)
print ("# sxx:",sxx)
print ("# ss:",ss)
print ("# stot(stot+1):",stot2)
if __name__ == "__main__":
main()