def signed_identity(n):
"""
returns the kronecker product of n signed identity 2 x 2 matrices
sI = [[1, 0],
[0, -1]]
out = sI \otimes sI \otimes sI \otimes .....
"""
sI = sm([[1, 0], [0, -1]])
out = sI.copy()
for x in xrange(n - 1):
out = kron(out, sI)
return out
def signed_identity(n):
"""
returns the kronecker product of n signed identity 2 x 2 matrices
sI = [[1, 0],
[0, -1]]
out = sI \otimes sI \otimes sI \otimes .....
"""
sI = sm([[1, 0], [0, -1]])
out = sI.copy()
for x in xrange(n - 1):
out = kron(out, sI)
return out
def f_destroy(n, Ntot):
"""
returns a fermionic descruction operator for the n'th single-particle
state out of N_tot states.
assumes that the states are ordered as:
|n_0, n_1, n_2, .... , n_(Ntot - 2), n_(Ntot - 1)>
"""
if n < 0 or n >= Ntot:
raise ValueError('n has to be in [0, 1, ..., Ntot - 1]')
# destruction operator for 1-state space
# |basis 0> = |0>, |basis 1> = c^+|0>,
c = sm([[0, 0], [1, 0]])
if n == 0:
return sm(kron(c, unsigned_identity(Ntot - 1)))
elif n == Ntot - 1:
return sm(kron(signed_identity(Ntot - 1), c))
else:
# signed identity and c
tmp = kron(signed_identity(n), c)
# this times unsigned indentity
return sm(kron(tmp, unsigned_identity(Ntot - 1 - n)))
def f_destroy(n, Ntot):
"""
returns a fermionic descruction operator for the n'th single-particle
state out of N_tot states.
assumes that the states are ordered as:
|n_0, n_1, n_2, .... , n_(Ntot - 2), n_(Ntot - 1)>
"""
if n < 0 or n >= Ntot:
raise ValueError('n has to be in [0, 1, ..., Ntot - 1]')
# destruction operator for 1-state space
# |basis 0> = |0>, |basis 1> = c^+|0>,
c = sm([[0, 0], [1, 0]])
if n == 0:
return sm(kron(c, unsigned_identity(Ntot - 1)))
elif n == Ntot - 1:
return sm(kron(signed_identity(Ntot - 1), c))
else:
# signed identity and c
tmp = kron(signed_identity(n), c)
# this times unsigned indentity
return sm(kron(tmp, unsigned_identity(Ntot - 1 - n)))
sys.path.insert(0, '.')
import squanf_class
Ne = 1
Nh = 1
eh = squanf_class.squanf(Ne=Ne, Nh=Nh, use_spin=True)
# short hands
e = eh.e
eD = eh.eD
h = eh.h
hD = eh.hD
# Hamiltonian
H = sm(e(0, 'u').shape)
Eex = 1.
V1 = 20.
V2 = 10.
for spin in ['u', 'd']:
H = H + Eex / 2 * eD(0, spin) * e(0, spin)
H = H + Eex / 2 * hD(0, spin) * h(0, spin)
print H.todense().astype(int)
