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hamiltonian.py
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hamiltonian.py
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from numpy import *
from copy import deepcopy
import graphene as grap
from edensity import *
from scipy.sparse import *
from scipy import *
def redand(bl):
return reduce(lambda x,y:x and y, bl)
class ham(object):
@property
def t0(self):return self.__t0
@property
def g(self): return self.__g
@property
def U(self): return self.__U
@property
def J(self): return self.__J
@property
def ed(self):return self.__ed
@ed.setter
def ed(self,newed):
self.__ed = newed
@property
def omg(self):return self.__omg
@property
def alp(self):return self.__alp
@property
def osc(self):return self.__osc
@property
def dim(self):return self.__dim
@property
def lstij(self):return self.__lstij
def __init__(self,width=6,length=10,boundary="open",holes=[],ledge=1.,
graphene=None, hopping=1.0,coulomb=1.3,
spincoupling=0.1, Ed=1.0, vibration=40.0, ssh=3.5 ):
if(graphene==None):
self.__g = grap.graphene(width,length,boundary,holes,ledge)
else:
self.__g = graphene
self.__t0 = hopping
self.__U = coulomb
self.__J = spincoupling
self.__ed = Ed
self.__omg = vibration
self.__alp = ssh
self.__osc = sum(
map(lambda x:reduce(self.g.ddispm,x)**2,
self.g.lslinks('1d')))
self.__nd = self.g.ndanglingc()
self.__nc = self.g.nvertex()
self.__dim = self.__nc# + self.__nd
self.__lstij = array(map( lambda x:map(self.p2i,x), self.g.lslinks('1d') ))
def lmd(self): return self.alp**2/self.t0/self.omg
def displace(self,p,d):
def f(x):
return self.g.isC(p) * self.g.ddispm(p,x)**2
pnb = self.g.pbneighb(p,'1d')
self.__osc -= sum(map(f,pnb))
self.g._displace(p,d)
self.__osc += sum(map(f,pnb))
def displacei(self,i,d):
p = self.i2p(i)
self.displace(p,d)
def diag(self,ip): #ip: index-pair of the matrix
if(not reduce(lambda x,y:x==y, ip)):
return 0
elif(redand(map(self.iinC,ip))):
return 1
else:
return 0
def Ht(self,ip):
if( redand(map(self.iinC,ip)) ):
pp = map(self.i2p,ip)
if( reduce(self.g.link,pp) ):
return -self.t0 * (1.0 - self.alp*reduce(self.g.ddistance,pp))
return 0.
else:
return 0.
def Hu(self,spin,eden,ip):
i = ip[0]
tmp = 0
if(self.iinC(i)):
tmp = eden.eden[flip(spin),i] #<n>n term
tmp -= reduce(dot,eden.eden) #<n><n> term
return self.U * tmp
def Hj(self,spin,eden,ip):
tmp = 0.
i = ip[0]
j = ip[1]
di = map(self.p2i, self.g.danglingc('1d')) #dangling vertece
dd = xrange(self.__nc,self.__dim+self.__nd) #dangling spins
tmp += dot( map(eden.spin, di), map(eden.spin, dd) ) # <S><S> term
#tmp -= sum(map(lambda x:x**2, eden.V)) /2. # V^2 term
spin = 1 if spin else 0 # make sure spin is 1 or 0
if(i in di):
tmp -= (-1)**(spin+1)/2. * eden.spin(self.i2id(i)) # <S>Sd terms
#if(i in dd):
# tmp -= (-1)**(spin+1) * eden.spin(self.id2i(i))/2. # <Sd>S terms
'''else:
if(i in di):
if(self.i2id(i)==j):
tmp -= eden.V[j-self.__nc]/2.
elif(i in dd):
if(self.id2i(i)==j):
tmp -= eden.V[i-self.__nc]/2.'''
return self.J * tmp
def Hd(self,ip):
if(redand(map(self.iind,ip)) and self.diag(ip) ):
return self.ed
else:
return 0.
def Ho(self,ip):
return self.omg * self.osc
def Hdia(self,spin,eden,ip):
if( not(redand(map(self.iinC,ip)) )):
return 0.
else:
return self.Hu(spin,eden,ip) + self.Ho(ip) + self.Hj(spin,eden,ip)
def Hall(self,spin,eden,ip):
return self.Ht(ip) + self.Hdia(spin,eden,ip)# + self.Hd(ip)
def matcsr(self,spin,eden):
return self.matcoo(spin,eden).tocsr()
def mat(self,spin,eden):
return self.matcoo(spin,eden).todense()
def matcoo(self,spin,eden):
#----initialization-----
ll = len(self.lstij)
n = self.dim + ll# + self.__nd
row = zeros(n,dtype=int)
dat = zeros(n,dtype=float)
#---------Hdia-----------
row[:self.dim] = xrange(self.dim)
col = deepcopy(row)
dat[:self.dim] = [self.Hdia(spin,eden,[i,i]) for i in xrange(self.dim)]
#----------Ht------------
col[self.dim:self.dim+ll], row[self.dim:self.dim+ll] = self.lstij.transpose()
#col[self.dim+ll:self.dim+2*ll], row[self.dim+ll:self.dim+2*ll] = self.lstij.transpose()
tmp = map(self.Ht, self.lstij)
dat[self.dim : self.dim+ll] = tmp
#dat[self.dim+ll : self.dim+2*ll] = tmp
#----------Hjo-----------
'''
if(self.__nd!=0):
di = map(self.p2i, self.g.danglingc('1d')) #dangling vertece
dd = xrange(self.__nc,self.__dim) #dangling spins
col[-self.__nd:] = di
row[-self.__nd:] = dd
#row[self.dim + 2*ll : self.dim + 2*ll + self.__nd] = di
#row[-self.__nd:] = dd
#col[self.dim + 2*ll : self.dim + 2*ll + self.__nd] = dd
#col[-self.__nd:] = di
tmp = [self.Hall(spin,eden,[di[i],dd[i]]) for i in xrange(self.__nd)]
#dat[self.dim + 2*ll : self.dim + 2*ll + self.__nd] = tmp
dat[-self.__nd:] = tmp
'''
return coo_matrix( (dat,(row,col)), shape=(self.dim,self.dim) )
#---------------------------------------------------------------#
def p2i(self,p):
#p = self.g.pnt(p,'1d')
return self.g.p2i[p]
#h = self.g.holes('1d')
#if(p in h):
# return None
# else:
# return p - len(filter(lambda x:x<p,h))
def i2p(self,i,form='1d'):
if(form=='1d'):
return self.g.i2p[i]
else:
return self.g.pnt(self.g.i2p[i],form)
'''
h = self.g.holes('1d')
lenh = self.g.nholes()
if(self.g.holes('1d')==[]):
p = i
elif(h[0]>i):
p = i
elif(h[-1]-lenh<i):
p = i+lenh
else:
k = 0
while(not(h[k]-k<i+1 and i+1<=h[k+1]-k-1)):
k += 1
p = i + k+1
if(form=='1d'):
return p
else:
return self.g.pnt(p,form)
'''
def iinC(self,i):
return 1 if(0<=i and i<self.__nc) else 0
def iind(self,i):
return 1 if(self.__nc<=i and i<self.__nc+self.__nd) else 0
def iinCd(self,i):
return 1 if(0<=i and i<self.__dim) else 0
def id2p(self,i,form='1d'):
if not self.iind(i):
try: 1/0
except: print "id2p: i not a dangling point"
raise
else:
return self.g.danglingc(form)[i-self.__nc]
def id2i(self,i):
return self.p2i(self.id2p(i))
def p2id(self,d):
#d = self.g.pnt(d,'1d')
i = list(self.g.danglingc('1d')).index(d)
return i + self.__nc
def i2id(self,i):
return self.p2id(self.i2p(i))