def _transl2fermi(self, tensor: Tensor):
"""Translate a tensor object in terms of the fermion operators.
This is an internally utility. The resulted tensor has the internal
fermion drudge object as its owner.
"""
return Tensor(self._ph_dr, tensor.subst_all(self._defs).terms)
def eval_vev(self, tensor: Tensor):
r"""Evaluate the vacuum expectation value.
The VEV facility works *as if* we do substitution
.. math::
P_p &= c_{p \downarrow} c_{p \uparrow} \\
P^\dag_p &= c^\dag_{p \uparrow} c^\dag_{p \downarrow} \\
N_p &= c^\dag_{p \uparrow} c_{p \uparrow}
+ c^\dag_{p \downarrow} c_{p \downarrow} \\
for :math:`p` in either particle or hole range and evaluate the
expectation value with respect to the Fermi vacuum.
"""
transled = self._transl2fermi(tensor)
res = self._ph_dr.eval_fermi_vev(transled)
return Tensor(self, res.terms)
def eval_agp(self, tensor: Tensor, zlist):
r"""Evaluate the vacuum expectation value.
The AGP expectation value facility works *as if* we do substitution
Takes as input the list of z matrices
.. math::
\langle P^\dag_p P_q \rangle &= A^{(0)}_{pq} \\
\langle P^\dag_p N_r P_q \rangle &= A^{(1)}_{pqr} \\
\langle P^\dag_p P^\dag_q P_rP_s\rangle &= A^{(0)}_{pqrs} \\
"""
num_ = self.cartan
pdag_ = self.raise_
p_ = self.lower
def get_vev_of_term(term):
"""Return the vev mapping of the term"""
vecs = term.vecs
t_amp = term.amp
pdag_cnt = 0
p_cnt = 0
n_cnt = 0
pdag_indlist = []
p_indlist = []
n_indlist = []
if len(vecs) == 0:
return [
Term(sums=term.sums, amp=t_amp * zlist[0][0], vecs=vecs)
]
# Classify the indices into pdag, n, and p indicies
for i in vecs:
if i.base == pdag_:
pdag_indlist.extend(list(i.indices))
elif i.base == p_:
p_indlist.extend(list(i.indices))
elif i.base == num_:
n_indlist.extend(list(i.indices))
else:
return []
# Count the number of indices
pdag_cnt = len(pdag_indlist)
p_cnt = len(p_indlist)
# First, we extract only the unique N indices
unique_n_indlist = list(set(n_indlist))
n_cnt = len(unique_n_indlist)
# Introduce appropriate power of 2 in amplitude to include the effect
# of unique indices only being considered in N
ldiff = len(n_indlist) - len(unique_n_indlist)
t_amp *= 2**(ldiff)
if pdag_cnt != p_cnt:
# The expression must have equal number of Pdag's and P_'s
return []
elif len(pdag_indlist) != len(set(pdag_indlist)):
return []
elif len(p_indlist) != len(set(p_indlist)):
return []
else:
# Combining all the indices
indcs = pdag_indlist
indcs.extend(unique_n_indlist)
indcs.extend(p_indlist)
# Counting the different number of indices in order
# to select the right symbol 'asymb'
idx1 = int(n_cnt)
idx_ppdag = len(indcs) - n_cnt
idx2 = int((idx_ppdag / 2))
asymb = zlist[idx1][idx2]
t_amp = t_amp * asymb[indcs]
return [Term(sums=term.sums, amp=t_amp, vecs=())]
return tensor.bind(get_vev_of_term)
def eval_agp(self, tensor: Tensor, zlist):
r"""Evaluate the vacuum expectation value.
The AGP expectation value facility works *as if* we do substitution
Takes as input the list of z matrices
.. math::
\langle P^\dag_p P_q \rangle &= A^{(0)}_{pq} \\
\langle P^\dag_p N_r P_q \rangle &= A^{(1)}_{pqr} \\
\langle P^\dag_p P^\dag_q P_rP_s\rangle &= A^{(0)}_{pqrs} \\
"""
num_ = self.cartan
pdag_ = self.raise_
p_ = self.lower
def get_vev_of_term(term):
"""Return the vev mapping of the term"""
vecs = term.vecs
t_amp = term.amp
pdag_cnt = 0
p_cnt = 0
n_cnt = 0
pdag_indlist = []
p_indlist = []
n_indlist = []
if len(vecs) == 0:
return [Term(sums=term.sums, amp=t_amp, vecs=vecs)]
for i in vecs:
if i.base == pdag_:
pdag_cnt += 1
pdag_indlist.extend(list(i.indices))
elif i.base == p_:
p_cnt += 1
p_indlist.extend(list(i.indices))
elif i.base == num_:
n_cnt += 1
n_indlist.extend(list(i.indices))
else:
return []
if pdag_cnt != p_cnt:
# The expression must have equal number of Pdag's and P_'s
return []
elif len(pdag_indlist) != len(set(pdag_indlist)):
return []
elif len(p_indlist) != len(set(p_indlist)):
return []
else:
# Combining all the indices
indcs = pdag_indlist
indcs.extend(n_indlist)
indcs.extend(p_indlist)
# Counting the different number of indices in order
# to select the right symbol 'asymb'
idx1 = int(n_cnt)
idx_ppdag = len(indcs) - n_cnt
idx2 = int((idx_ppdag / 2))
asymb = zlist[idx1][idx2]
t_amp = t_amp * asymb[indcs]
return [Term(sums=term.sums, amp=t_amp, vecs=())]
return tensor.bind(get_vev_of_term)
def eval_awev (self, tensor: Tensor):
terms = self._eval_awev (tensor)
return Tensor (self, terms)