def __init__(self,Beta,Norb,U_interact,J_Hund) :
# NB : the Hamiltonian should NOT contain the quadratic part which is in G0
Hamiltonian = U_interact * Sum( [ N('up',i)*N('down',i) for i in range(Norb) ] )
for i in range(Norb-1):
for j in range(i+1,Norb):
Hamiltonian += (U_interact-2*J_Hund) * ( N('up',i) * N('down',j) +
N('down',i) * N('up',j) ) + \
(U_interact-3*J_Hund) * ( N('up',i) * N('up',j) +
N('down',i) * N('down',j) )
#Quantum_Numbers = {}
#for i in range(Norb):
# Quantum_Numbers['N%sup'%(i+1)] = N('up',i)
# Quantum_Numbers['N%sdown'%(i+1)] = N('down',i)
Ntot = Sum( [ N(s,i) for s in ['up','down'] for i in range(Norb) ] )
Sz = Sum( [ N('up',i)-N('down',i) for i in range(Norb) ] )
Quantum_Numbers = {'Ntot' : Ntot, 'Sz' : Sz}
Solver.__init__(self,
Beta = Beta,
GFstruct = [ ('%s'%(ud),[n for n in range(Norb)]) for ud in ['up','down'] ],
H_Local = Hamiltonian,
Quantum_Numbers = Quantum_Numbers )
self.N_Cycles = 10000
def __init__(self,Beta,U_interact,J_Hund) :
GFstruct = [ ('1up',[1]), ('1down',[1]), ('23up',[1,2]), ('23down',[1,2]) ]
# NB : the Hamiltonian should NOT contain the quadratic part which is in G0
#Hamiltonian = U_interact * Sum( [ N('%d-up'%(i+1),1)*N('%d-down'%(i+1),1) for i in range(3) ] )
Hamiltonian = U_interact * ( N('1up',1)*N('1down',1) + N('23up',1)*N('23down',1) + N('23up',2)*N('23down',2) )
Hamiltonian += (U_interact-2.0*J_Hund) * ( N('1up',1) * (N('23down',1)+N('23down',2)) + N('23up',1) * N('23down',2) )
Hamiltonian += (U_interact-2.0*J_Hund) * ( N('1down',1) * (N('23up',1)+N('23up',2)) + N('23up',2) * N('23down',1) )
for s in ['up','down']:
Hamiltonian += (U_interact-3.0*J_Hund) * (N('1%s'%s,1) * (N('23%s'%s,1)+N('23%s'%s,2)) + N('23%s'%s,1)*N('23%s'%s,2) )
# for i in range(2):
# for j in range(i+1,3):
# Hamiltonian += (U_interact-2*J_Hund) * ( N('%d-up'%(i+1),1) * N('%d-down'%(j+1),1) +
# N('%d-down'%(i+1),1) * N('%d-up'%(j+1),1) ) + \
# (U_interact-3*J_Hund) * ( N('%d-up'%(i+1),1) * N('%d-up'%(j+1),1) +
# N('%d-down'%(i+1),1) * N('%d-down'%(j+1),1) )
# Quantum_Numbers = { 'N1up' : N('1-up',1), 'N1down' : N('1-down',1),
# 'N2up' : N('2-up',1), 'N2down' : N('2-down',1),
# 'N3up' : N('3-up',1), 'N3down' : N('3-down',1) }
Quantum_Numbers = { 'N1up' : N('1up',1), 'N1down' : N('1down',1),
'N23up' : N('23up',1)+N('23up',2),
'N23down' : N('23down',1)+N('23down',2) }
Solver.__init__(self,
Beta = Beta,
GFstruct = GFstruct,
H_Local = Hamiltonian,
Quantum_Numbers = Quantum_Numbers )
self.N_Cycles = 10000
def __init__(self,Beta,U_interact) :
self.P = numpy.array([[1,1,1,1], [1,-1,1,-1],[1,1,-1,-1],[1,-1,-1,1]])/2.
self.Pinv = numpy.linalg.inv(self.P)
def Cdiag(s):
s= '-%s'%s
return [ C('00'+s,1), C('10'+s,1), C('01'+s,1),C('11'+s,1) ]
Cnat,Nnat={},{}
for i in range(4) :
s= 'up-%d'%(i+1)
Cnat[s] = Sum( [ self.P[i,j]*c for j,c in enumerate(Cdiag('up'))] )
Nnat[s] = Cnat[s].dagger() * Cnat[s]
s= 'down-%d'%(i+1)
Cnat[s] = Sum( [ self.P[i,j]*c for j,c in enumerate(Cdiag('down'))] )
Nnat[s] = Cnat[s].dagger() * Cnat[s]
def symm(s):
s= '-%s'%s
Cdag('00'+s,1).Symmetry()['kx'] = 1
Cdag('10'+s,1).Symmetry()['kx'] = -1
Cdag('01'+s,1).Symmetry()['kx'] = 1
Cdag('11'+s,1).Symmetry()['kx'] = -1
Cdag('00'+s,1).Symmetry()['ky'] = 1
Cdag('10'+s,1).Symmetry()['ky'] = 1
Cdag('01'+s,1).Symmetry()['ky'] = -1
Cdag('11'+s,1).Symmetry()['ky'] = -1
symm('up'); symm('down')
# NB : the Hamiltonian should NOT contain the quadratic part which is in G0
Hamiltonian = U_interact* Sum( [ Nnat['up-%d'%(i+1)]* Nnat['down-%d'%(i+1)] for i in range (4)])
N_u = Sum( [ Nnat['up-%d'%(i+1)] for i in range(4) ] )
N_d = Sum( [ Nnat['down-%d'%(i+1)] for i in range(4) ] )
Quantum_Numbers = { 'kx' : 'kx', 'ky' : 'ky', 'N_u' : N_u, 'N_d' : N_d }
Solver.__init__(self,
Beta = Beta,
GFstruct = [ ('00-up',[1]), ('10-up',[1]), ('01-up',[1]), ('11-up',[1]),
('00-down',[1]), ('10-down',[1]), ('01-down',[1]), ('11-down',[1]) ],
H_Local = Hamiltonian,
Quantum_Numbers = Quantum_Numbers,
Nmax = 2000)
self.N_Cycles = 100000
self.N_Frequencies_Accumulated = 4*int(0.075*Beta/(2*3.1415))
self.Fitting_Frequency_Start = 3*int(0.075*Beta/(2*3.1415))
self.Length_Cycle = 100
self.Nmax_Matrix = 200
self.Use_Segment_Picture = False
def __init__(self,Beta,U_interact) :
Hamiltonian = U_interact*( N('1-up',1)*N('1-down',1) + N('1-up',1)*N('2-up',1) +
N('1-up',1)*N('2-down',1) + N('1-down',1)*N('2-up',1) +
N('1-down',1)*N('2-down',1) + N('2-up',1)*N('2-down',1) )
Quantum_Numbers = { 'Nup' : N('1-up',1)+N('2-up',1),
'Ndown' : N('1-down',1)+N('2-down',1),
'Lz' : N('1-up',1)+N('1-down',1)-N('2-up',1)-N('2-down',1) }
Solver.__init__(self,
Beta = Beta,
GFstruct = [ ('1-up',[1]), ('1-down',[1]), ('2-up',[1]), ('2-down',[1]) ],
H_Local = Hamiltonian,
Quantum_Numbers = Quantum_Numbers )
self.N_Cycles = 1000000
self.Nmax_Matrix = 300
def __init__(self,Beta,U_interact) :
self.P = numpy.array([[1,1,1,1], [1,-1,1,-1],[1,1,-1,-1],[1,-1,-1,1]])/2.
self.Pinv = numpy.linalg.inv(self.P)
def Cdiag(s):
s= '-%s'%s
return [ C('00'+s,1), C('10'+s,1), C('01'+s,1),C('11'+s,1) ]
Cnat,Nnat={},{}
for i in range(4) :
s= 'up-%d'%(i+1)
Cnat[s] = Sum( [ self.P[i,j]*c for j,c in enumerate(Cdiag('up'))] )
Nnat[s] = Cnat[s].dagger() * Cnat[s]
s= 'down-%d'%(i+1)
Cnat[s] = Sum( [ self.P[i,j]*c for j,c in enumerate(Cdiag('down'))] )
Nnat[s] = Cnat[s].dagger() * Cnat[s]
def symm(s):
s= '-%s'%s
Cdag('00'+s,1).Symmetry()['kx'] = 1
Cdag('10'+s,1).Symmetry()['kx'] = -1
Cdag('01'+s,1).Symmetry()['kx'] = 1
Cdag('11'+s,1).Symmetry()['kx'] = -1
Cdag('00'+s,1).Symmetry()['ky'] = 1
Cdag('10'+s,1).Symmetry()['ky'] = 1
Cdag('01'+s,1).Symmetry()['ky'] = -1
Cdag('11'+s,1).Symmetry()['ky'] = -1
symm('up'); symm('down')
# NB : the Hamiltonian should NOT contain the quadratic part which is in G0
Hamiltonian = U_interact* Sum( [ Nnat['up-%d'%(i+1)]* Nnat['down-%d'%(i+1)] for i in range (4)]) #!!
N_u = Sum( [ Nnat['up-%d'%(i+1)] for i in range(4) ] )
N_d = Sum( [ Nnat['down-%d'%(i+1)] for i in range(4) ] )
Quantum_Numbers = { 'kx' : 'kx', 'ky' : 'ky', 'N_u' : N_u, 'N_d' : N_d }
Solver.__init__(self,Beta=Beta,GFstruct=[ ('00-up',[1]), ('10-up',[1]), ('01-up',[1]), ('11-up',[1]),
('00-down',[1]), ('10-down',[1]), ('01-down',[1]), ('11-down',[1]) ],
H_Local = Hamiltonian,Quantum_Numbers= Quantum_Numbers )
self.N_Cycles = 10
def __init__(self,Beta,U_interact) :
C_up_1 = (C('Up+',1) + C('Up-',1))/sqrt(2)
C_up_2 = (C('Up+',1) - C('Up-',1))/sqrt(2)
C_do_1 = (C('Do+',1) + C('Do-',1))/sqrt(2)
C_do_2 = (C('Do+',1) - C('Do-',1))/sqrt(2)
Cdag('Up+',1).Symmetry()['parity'] = 1
Cdag('Up-',1).Symmetry()['parity'] = -1
Cdag('Do+',1).Symmetry()['parity'] = 1
Cdag('Do-',1).Symmetry()['parity'] = -1
N_up_1 = C_up_1.dagger()*C_up_1
N_up_2 = C_up_2.dagger()*C_up_2
N_do_1 = C_do_1.dagger()*C_do_1
N_do_2 = C_do_2.dagger()*C_do_2
# NB : the Hamiltonian should NOT contain the quadratic part which is in G0
Hamiltonian = U_interact * ( N_up_1*N_do_1 + N_up_2*N_do_2 )
N_u = N('Up-',1)+N('Up+',1)
N_d = N('Do-',1)+N('Do+',1)
Quantum_Numbers = { 'parity' : 'parity', 'N_u' : N_u, 'N_d' : N_d }
Solver.__init__(self,
Beta = Beta,
GFstruct = [ ('Up+',[1]), ('Up-',[1]), ('Do+',[1]), ('Do-',[1]) ],
H_Local = Hamiltonian,
Quantum_Numbers = Quantum_Numbers,
Nmax = 2000)
self.N_Cycles = 100000
self.N_Frequencies_Accumulated = 4*int(0.075*Beta/(2*3.1415))
self.Fitting_Frequency_Start = 3*int(0.075*Beta/(2*3.1415))
self.Length_Cycle = 100
self.Nmax_Matrix = 200
self.Use_Segment_Picture = False
def __init__(self,
Beta,
Norb,
U_interact=None,
J_Hund=None,
GFStruct=False,
map=False,
use_spinflip=False,
useMatrix=True,
l=2,
T=None,
dimreps=None,
irep=None,
deg_orbs=[],
Sl_Int=None):
self.offset = 0
self.use_spinflip = use_spinflip
self.Norb = Norb
if (useMatrix):
if not (Sl_Int is None):
Umat = Umatrix(l=l)
assert len(Sl_Int) == (l + 1), "Sl_Int has the wrong length"
if (type(Sl_Int) == ListType):
Rcl = numpy.array(Sl_Int)
else:
Rcl = Sl_Int
Umat(T=T, Rcl=Rcl)
else:
if ((U_interact == None) and (J_Hund == None)):
MPI.report("Give U,J or Slater integrals!!!")
assert 0
Umat = Umatrix(U_interact=U_interact, J_Hund=J_Hund, l=l)
Umat(T=T)
Umat.ReduceMatrix()
if (Umat.N == Umat.Nmat):
# Transformation T is of size 2l+1
self.U = Umat.U
self.Up = Umat.Up
else:
# Transformation is of size 2(2l+1)
self.U = Umat.U
# now we have the reduced matrices U and Up, we need it for tail fitting anyways
if (use_spinflip):
#Take the 4index Umatrix
# check for imaginary matrix elements:
if (abs(Umat.Ufull.imag) > 0.0001).any():
MPI.report(
"WARNING: complex interaction matrix!! Ignoring imaginary part for the moment!"
)
MPI.report(
"If you want to change this, look into Wien2k/Solver_MultiBand.py"
)
self.U4ind = Umat.Ufull.real
# this will be changed for arbitrary irep:
# use only one subgroup of orbitals?
if not (irep is None):
#print irep, dimreps
assert not (dimreps is None
), "Dimensions of the representatives are missing!"
assert Norb == dimreps[
irep - 1], "Dimensions of dimrep and Norb do not fit!"
for ii in range(irep - 1):
self.offset += dimreps[ii]
else:
if ((U_interact == None) and (J_Hund == None)):
MPI.report("For Kanamori representation, give U and J!!")
assert 0
self.U = numpy.zeros([Norb, Norb], numpy.float_)
self.Up = numpy.zeros([Norb, Norb], numpy.float_)
for i in range(Norb):
for j in range(Norb):
if (i == j):
self.Up[i, i] = U_interact + 2.0 * J_Hund
else:
self.Up[i, j] = U_interact
self.U[i, j] = U_interact - J_Hund
if (GFStruct):
assert map, "give also the mapping!"
self.map = map
else:
# standard GFStruct and map
GFStruct = [('%s' % (ud), [n for n in range(Norb)])
for ud in ['up', 'down']]
self.map = {
'up': ['up' for v in range(self.Norb)],
'down': ['down' for v in range(self.Norb)]
}
#print GFStruct,self.map
if (use_spinflip == False):
Hamiltonian = self.__setHamiltonian_density()
else:
if (useMatrix):
Hamiltonian = self.__setfullHamiltonian_Slater()
else:
Hamiltonian = self.__setfullHamiltonian_Kanamori(J_Hund=J_Hund)
Quantum_Numbers = self.__setQuantumNumbers(GFStruct)
# Determine if there are only blocs of size 1:
self.blocssizeone = True
for ib in GFStruct:
if (len(ib[1]) > 1): self.blocssizeone = False
# now initialize the solver with the stuff given above:
Solver.__init__(self,
Beta=Beta,
GFstruct=GFStruct,
H_Local=Hamiltonian,
Quantum_Numbers=Quantum_Numbers)
#self.SetGlobalMoves(deg_orbs)
self.N_Cycles = 10000
self.Nmax_Matrix = 100
self.N_Time_Slices_Delta = 10000
#if ((len(GFStruct)==2*Norb) and (use_spinflip==False)):
if ((self.blocssizeone) and (use_spinflip == False)):
self.Use_Segment_Picture = True
else:
self.Use_Segment_Picture = False
def __init__(self, Beta, Norb, U_interact=None, J_Hund=None, GFStruct=False, map=False, use_spinflip=False,
useMatrix = True, l=2, T=None, dimreps=None, irep=None, deg_orbs = [], Sl_Int = None):
self.offset = 0
self.use_spinflip = use_spinflip
self.Norb = Norb
if (useMatrix):
if not (Sl_Int is None):
Umat = Umatrix(l=l)
assert len(Sl_Int)==(l+1),"Sl_Int has the wrong length"
if (type(Sl_Int)==ListType):
Rcl = numpy.array(Sl_Int)
else:
Rcl = Sl_Int
Umat(T=T,Rcl=Rcl)
else:
if ((U_interact==None)and(J_Hund==None)):
MPI.report("Give U,J or Slater integrals!!!")
assert 0
Umat = Umatrix(U_interact=U_interact, J_Hund=J_Hund, l=l)
Umat(T=T)
Umat.ReduceMatrix()
if (Umat.N==Umat.Nmat):
# Transformation T is of size 2l+1
self.U = Umat.U
self.Up = Umat.Up
else:
# Transformation is of size 2(2l+1)
self.U = Umat.U
# now we have the reduced matrices U and Up, we need it for tail fitting anyways
if (use_spinflip):
#Take the 4index Umatrix
# check for imaginary matrix elements:
if (abs(Umat.Ufull.imag)>0.0001).any():
MPI.report("WARNING: complex interaction matrix!! Ignoring imaginary part for the moment!")
MPI.report("If you want to change this, look into Wien2k/Solver_MultiBand.py")
self.U4ind = Umat.Ufull.real
# this will be changed for arbitrary irep:
# use only one subgroup of orbitals?
if not (irep is None):
#print irep, dimreps
assert not (dimreps is None), "Dimensions of the representatives are missing!"
assert Norb==dimreps[irep-1],"Dimensions of dimrep and Norb do not fit!"
for ii in range(irep-1):
self.offset += dimreps[ii]
else:
if ((U_interact==None)and(J_Hund==None)):
MPI.report("For Kanamori representation, give U and J!!")
assert 0
self.U = numpy.zeros([Norb,Norb],numpy.float_)
self.Up = numpy.zeros([Norb,Norb],numpy.float_)
for i in range(Norb):
for j in range(Norb):
if (i==j):
self.Up[i,i] = U_interact + 2.0*J_Hund
else:
self.Up[i,j] = U_interact
self.U[i,j] = U_interact - J_Hund
if (GFStruct):
assert map, "give also the mapping!"
self.map = map
else:
# standard GFStruct and map
GFStruct = [ ('%s'%(ud),[n for n in range(Norb)]) for ud in ['up','down'] ]
self.map = {'up' : ['up' for v in range(self.Norb)], 'down' : ['down' for v in range(self.Norb)]}
#print GFStruct,self.map
if (use_spinflip==False):
Hamiltonian = self.__setHamiltonian_density()
else:
if (useMatrix):
Hamiltonian = self.__setfullHamiltonian_Slater()
else:
Hamiltonian = self.__setfullHamiltonian_Kanamori(J_Hund = J_Hund)
Quantum_Numbers = self.__setQuantumNumbers(GFStruct)
# Determine if there are only blocs of size 1:
self.blocssizeone = True
for ib in GFStruct:
if (len(ib[1])>1): self.blocssizeone = False
# now initialize the solver with the stuff given above:
Solver.__init__(self,
Beta = Beta,
GFstruct = GFStruct,
H_Local = Hamiltonian,
Quantum_Numbers = Quantum_Numbers )
#self.SetGlobalMoves(deg_orbs)
self.N_Cycles = 10000
self.Nmax_Matrix = 100
self.N_Time_Slices_Delta= 10000
#if ((len(GFStruct)==2*Norb) and (use_spinflip==False)):
if ((self.blocssizeone) and (use_spinflip==False)):
self.Use_Segment_Picture = True
else:
self.Use_Segment_Picture = False
