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ed_sz_conserved_2d_heisenberg_J1J2_square_spin_corr.py
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ed_sz_conserved_2d_heisenberg_J1J2_square_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 square for a given Sz')
parser.add_argument('-Lx', metavar='Lx',dest='Lx', type=int, default=4, help='set Lx (should be >=2)')
parser.add_argument('-Ly', metavar='Ly',dest='Ly', type=int, default=4, help='set Ly (should be >=2)')
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')
parser.add_argument('-Sz', metavar='Sz',dest='Sz', type=int, default=0, help='set Sz')
return parser.parse_args()
def snoob(x):
next = 0
if(x>0):
smallest = x & -(x)
ripple = x + smallest
ones = x ^ ripple
ones = (ones >> 2) // smallest
next = ripple | ones
return next
def binomial(n,r):
return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
def count_bit(n):
count = 0
while (n):
count += n & 1
n >>= 1
return count
def init_parameters(N,Sz):
Nup = N//2 + Sz
Nhilbert = binomial(N,Nup)
ihfbit = 1 << (N//2)
irght = ihfbit-1
ilft = ((1<<N)-1) ^ irght
iup = (1<<(N-Nup))-1
return Nup, Nhilbert, ihfbit, irght, ilft, iup
def make_list(N,Nup,Nhilbert,ihfbit,irght,ilft,iup):
list_1 = np.zeros(Nhilbert,dtype=int)
list_ja = np.zeros(ihfbit,dtype=int)
list_jb = np.zeros(ihfbit,dtype=int)
ii = iup
ja = 0
jb = 0
ia_old = ii & irght
ib_old = (ii & ilft) // ihfbit
list_1[0] = ii
list_ja[ia_old] = ja
list_jb[ib_old] = jb
ii = snoob(ii)
for i in range(1,Nhilbert):
ia = ii & irght
ib = (ii & ilft) // ihfbit
if (ib == ib_old):
ja += 1
else:
jb += ja+1
ja = 0
list_1[i] = ii
list_ja[ia] = ja
list_jb[ib] = jb
ia_old = ia
ib_old = ib
ii = snoob(ii)
return list_1, list_ja, list_jb
def get_ja_plus_jb(ii,irght,ilft,ihfbit,list_ja,list_jb):
ia = ii & irght
ib = (ii & ilft) // ihfbit
ja = list_ja[ia]
jb = list_jb[ib]
return ja+jb
def make_hamiltonian(Jxx,Jzz,list_isite1,list_isite2,N,Nint,Nhilbert,irght,ilft,ihfbit,list_1,list_ja,list_jb):
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]
## calculate elements of
## H_loc = Jzz sgmz.sgmz + Jxx (sgmx.sgmx + sgmy.sgmy)
## = Jzz sgmz.sgmz + 2*Jxx (S+.S- + S-.S+)
for i in range(Nhilbert): # loop for all spin configurations with fixed Sz
ii = list_1[i]
ibit = ii & is12 # find sgmz.sgmz|uu> = |uu> or sgmz.sgmz|dd> = |dd>
loc[Nint*Nhilbert+i] = i # store diag index
if (ibit==0 or ibit==is12): # if (spin1,spin2) = (00) or (11): sgmz.sgmz only
elemnt[Nint*Nhilbert+i] += diag # store +Jzz
# print("# diag k(interactions) i(Hilbert)",k,i)
# print("# diag ii ",np.binary_repr(ii,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): sgmz.sgmz and (S+.S- or S-.S+)
elemnt[Nint*Nhilbert+i] -= diag # store -Jzz
iexchg = ii ^ is12 # find S+.S-|du> = |ud> or S-.S+|ud> = |du>
newcfg = get_ja_plus_jb(iexchg,irght,ilft,ihfbit,list_ja,list_jb)
elemnt[k*Nhilbert+i] = wght # store 2*Jxx
loc[k*Nhilbert+i] = newcfg # store offdiag index
# print("# offdiag k(interactions) i(Hilbert)",k,i)
# print("# offdiag ii ",np.binary_repr(ii,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,list_1):
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 with fixed Sz
ii = list_1[i]
ibit = ii & is12 # find sgmz.sgmz|uu> = |uu> or sgmz.sgmz|dd> = |dd>
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*psi[i]**2 # psi[i]: real
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,irght,ilft,ihfbit,list_1,list_ja,list_jb):
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 with fixed Sz
ii = list_1[i]
ibit = ii & is12 # find sgmz.sgmz|ud> = -|ud> or sgmz.sgmz|du> = -|du>
if (ibit==is1 or ibit==is2): # if (spin1,spin2) = (10) or (01)
iexchg = ii ^ is12 # find S+.S-|du> = |ud> or S-.S+|ud> = |du>
newcfg = get_ja_plus_jb(iexchg,irght,ilft,ihfbit,list_ja,list_jb)
corr += psi[i]*psi[newcfg] # psi[i]: real
sxx[k] = 0.25 * corr
if (isite1==isite2):
sxx[k] = 0.25
return sxx
def make_lattice(Lx,Ly,J1,J2):
Jxx = []
Jzz = []
list_isite1 = []
list_isite2 = []
Nint = 0
for iy in range(Ly):
for ix in range(Lx):
site1 = ix + Lx*iy
site1x = (ix+1)%Lx + Lx*iy
site1y = ix + Lx*((iy+1)%Ly)
site1xpy = (ix+1)%Lx + Lx*((iy+1)%Ly)
site1xmy = (ix+1)%Lx + Lx*((iy-1+Ly)%Ly)
#
list_isite1.append(site1)
list_isite2.append(site1x)
Jxx.append(J1)
Jzz.append(J1)
Nint += 1
#
list_isite1.append(site1)
list_isite2.append(site1y)
Jxx.append(J1)
Jzz.append(J1)
Nint += 1
#
list_isite1.append(site1)
list_isite2.append(site1xpy)
Jxx.append(J2)
Jzz.append(J2)
Nint += 1
#
list_isite1.append(site1)
list_isite2.append(site1xmy)
Jxx.append(J2)
Jzz.append(J2)
Nint += 1
return Jxx, Jzz, list_isite1, list_isite2, Nint
def main():
args = parse_args()
Lx = args.Lx
Ly = args.Ly
N = Lx*Ly
Sz = args.Sz
J1 = args.J1
J2 = args.J2
Nup, Nhilbert, ihfbit, irght, ilft, iup = init_parameters(N,Sz)
binirght = np.binary_repr(irght,width=N)
binilft = np.binary_repr(ilft,width=N)
biniup = np.binary_repr(iup,width=N)
print("Lx=",Lx)
print("Ly=",Ly)
print("J1=",J1)
print("J2=",J2)
print("N=",N)
print("Sz=",Sz)
print("Nup=",Nup)
print("Nhilbert=",Nhilbert)
print("ihfbit=",ihfbit)
print("irght,binirght=",irght,binirght)
print("ilft,binilft=",ilft,binilft)
print("iup,biniup=",iup,biniup)
start = time.time()
list_1, list_ja, list_jb = make_list(N,Nup,Nhilbert,ihfbit,irght,ilft,iup)
end = time.time()
print (end - start)
# print("list_1=",list_1)
# print("list_ja=",list_ja)
# print("list_jb=",list_jb)
print("")
# print("i ii binii ja+jb")
# for i in range(Nhilbert):
# ii = list_1[i]
# binii = np.binary_repr(ii,width=N)
# ind = get_ja_plus_jb(ii,irght,ilft,ihfbit,list_ja,list_jb)
# print(i,ii,binii,ind)
Jxx, Jzz, list_isite1, list_isite2, Nint = make_lattice(Lx,Ly,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,irght,ilft,ihfbit,list_1,list_ja,list_jb)
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)
ene = ene/N/4
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):
# ii = list_1[i]
# binii = np.binary_repr(ii,width=N)
# print (i,vec[i,0]*vec_sgn,binii)
#
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,list_1)
sxx = calc_xcorr(Nhilbert,Ncorr,list_corr_isite1,list_corr_isite2,psi,irght,ilft,ihfbit,list_1,list_ja,list_jb)
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()