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makematrix_sparse.py
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makematrix_sparse.py
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#make matrix rep of hamiltonan
import numpy as np
from scipy.sparse import lil_matrix
import itertools
def Braket(basisseq,column,row,spin):
braket=np.hstack((np.fliplr(basisseq[row])[spin],basisseq[column,spin]))
return braket
def Parity(sitesize,diff,braket):# fermion sign
#site number of an electron ani
anidex=np.asscalar(np.array((np.where(diff==1))))
#site number of electron cre
cridex=np.asscalar(np.array((np.where(diff==-1))))
overelecnum=sum(braket[sitesize-cridex:sitesize+anidex])
if overelecnum%2==0:#whether the number of overjump cre op. is even or not
parity=1
else:
parity=-1
return parity
def MatrixRep(sitesize,basisseq,basissize,t1,t2,U,V1,V2,bc):
MR=lil_matrix((basissize,basissize))#initialization
for i, j in itertools.product(range(basissize), range(basissize)):
#for i in range(basissize):
#for j in range(basissize):
Diff =basisseq[i]-basisseq[j]
if (Diff[0]==0).all():
if (Diff[1]==0).all():#diagonal elements
MR[i,j]+=U*np.array(np.where(sum(basisseq[i],0)==2)).size#onsite interaction
for l in range(sitesize-1):#NNinteraction(nonBoundary)
MR[i,j]+=V1*sum(basisseq[i],0)[l]*sum(basisseq[i],0)[l+1]
MR[i,j]+=V1*sum(basisseq[i],0)[sitesize-1]*sum(basisseq[i],0)[0]*bc*bc#NNinteraction(boundary)
for m in range(sitesize-2):#NNNinteraction(nonboundary)
MR[i,j]+=V2*sum(basisseq[i],0)[m]*sum(basisseq[i],0)[m+2]
MR[i,j]+=V2*sum(basisseq[i],0)[sitesize-2]*sum(basisseq[i],0)[0]*bc*bc#NNNinteraction(boundary)1
MR[i,j]+=V2*sum(basisseq[i],0)[sitesize-1]*sum(basisseq[i],0)[1]*bc*bc#NNNinteraction(boundary)2
else: #downhopping
if np.array(np.nonzero(Diff[1])).size==2:
#exclude many electrons hopping concurrently
if abs(np.array(np.nonzero(Diff[1]))[0,0]-np.array(np.nonzero(Diff[1]))[0,1])==1:
#NNhopping(NonBoundary)
bk=Braket(basisseq,i,j,1)
MR[i,j]+=-t1*Parity(sitesize,Diff[1],bk)
elif abs(np.array(np.nonzero(Diff[1]))[0,0]-np.array(np.nonzero(Diff[1]))[0,1])==2:
#NNNhopping(Nonboundary)
bk=Braket(basisseq,i,j,1)
MR[i,j]+=-t2*Parity(sitesize,Diff[1],bk)
if abs(np.array(np.nonzero(Diff[1]))[0,0]-np.array(np.nonzero(Diff[1]))[0,1])==sitesize-1:
#NNhopping(Boundary)
bk=Braket(basisseq,i,j,1)
MR[i,j]+=-t1*bc*Parity(sitesize,Diff[1],bk)
elif abs(np.array(np.nonzero(Diff[1]))[0,0]-np.array(np.nonzero(Diff[1]))[0,1])==sitesize-2:
#NNNhopping(Boundary)
bk=Braket(basisseq,i,j,1)
MR[i,j]+=-t2*bc*Parity(sitesize,Diff[1],bk)
else:
if (Diff[1]==0).all():#uphopping
if np.array(np.nonzero(Diff[0])).size==2:
#exclude many electrons hopping concurrently
if abs(np.array(np.nonzero(Diff[0]))[0,0]-np.array(np.nonzero(Diff[0]))[0,1])==1:
#NNhopping(NonBoundary)
bk=Braket(basisseq,i,j,0)
MR[i,j]+=-t1*Parity(sitesize,Diff[0],bk)
elif abs(np.array(np.nonzero(Diff[0]))[0,0]-np.array(np.nonzero(Diff[0]))[0,1])==2:
#NNNhopping(Nonboundary)
bk=Braket(basisseq,i,j,0)
MR[i,j]+=-t2*Parity(sitesize,Diff[0],bk)
if abs(np.array(np.nonzero(Diff[0]))[0,0]-np.array(np.nonzero(Diff[0]))[0,1])==sitesize-1:
#NNhopping(Boundary)
bk=Braket(basisseq,i,j,0)
MR[i,j]+=-t1*bc*Parity(sitesize,Diff[0],bk)
elif abs(np.array(np.nonzero(Diff[0]))[0,0]-np.array(np.nonzero(Diff[0]))[0,1])==sitesize-2:
#NNNhopping(Boundary)
bk=Braket(basisseq,i,j,0)
MR[i,j]+=-t2*bc*Parity(sitesize,Diff[0],bk)
MR=MR.tocsr()
return MR
if __name__ == '__main__':
import makebasis as mb
hop1=10#NN hopping
hop2=1#NNN hopping
U=100#onsite interaction
Vint1=10#NN interaction
Vint2=1#NNN interaction
BC=1#coeffiient of boundary conditon(PBC＝１,APBC=-1,OBC=0)
SiteSize=8
ElecSize=4
TotalSpin=0
BasisSeq,BasisSize=mb.BasisSeqSize(SiteSize,ElecSize,TotalSpin)
H=MatrixRep(SiteSize,BasisSeq,BasisSize,hop1,hop2,U,Vint1,Vint2,BC)