def _transl2uga(self, tensor: Tensor):
"""Translate a tensor object in terms of the fermion operators.
This is an internal utility. The resulting tensor has the internal
'_uga_dr' drudge object as its owner.
"""
return Tensor(self, tensor.subst_all(self._agp2uga_defs).terms)
def _transl2uga(self, tensor: Tensor):
"""Translate a tensor object in terms of the fermion operators.
This is an internal utility. The resulting tensor has the internal
AGP drudge object as its owner.
"""
chk = tensor.bind(self._agp_dr._isAGP)
# for t in trms:
# if ~self._agp_dr._isAGP(t):
# raise ValueError('Unexpected generator of the AGP Algebra',vec)
return Tensor(self, tensor.subst_all(self._agp2uga_defs).terms)
def _transl2agp(self, tensor: Tensor):
"""Translate a tensor object in terms of the fermion operators.
This is an internal utility. The resulting tensor has the internal
AGP drudge object as its owner.
"""
chk = tensor.bind(self._isUGA)
# for t in trms:
# if ~_isUGA(t):
# raise ValueError('Unexpected generator of the Unitary Group',vec)
return Tensor(self._agp_dr, tensor.subst_all(self._uga2agp_defs).terms)
def spin_flip_to_fermi(self, tnsr: Tensor):
"""Substitute all the Spin flip operators with their respective fermionic
strings"""
gen_idx = self.all_orb_dumms[0]
sp_def = self.define(
SPIN_RAISE, gen_idx,
cr[gen_idx, SpinOneHalf.UP] * an[gen_idx, SpinOneHalf.DOWN])
sm_def = self.define(
SPIN_LOWER, gen_idx,
cr[gen_idx, SpinOneHalf.DOWN] * an[gen_idx, SpinOneHalf.UP])
spin_defs = [sp_def, sm_def]
return Tensor(self, tnsr.subst_all(spin_defs).terms)
def get_vev(self, h_tsr: Tensor):
"""Function to evaluate the expectation value of a normal
ordered tensor 'h_tsr' with respect to the projected BCS
ground state
h_tsr = tensor whose VEV is to be evaluated
Ntot = total number of orbitals available
Note that here we follow the notation that Np = Number of Fermions and not number of pairs
"""
ctan = self.cartan
gam = IndexedBase(r'\gamma')
def vev_of_term(term):
"""Return the VEV of a given term"""
vecs = term.vecs
t_amp = term.amp
ind_list = []
if len(vecs) == 0:
return term
elif all(v.base == ctan for v in vecs):
for i in vecs:
if set(i.indices).issubset(set(ind_list)):
t_amp = t_amp * 2
# NOTE: This is only true when evaluating expectation over AGP,
# or any other seniority zero state
else:
ind_list.extend(list(i.indices))
else:
return []
t_amp = t_amp * gam[ind_list]
return [Term(sums=term.sums, amp=t_amp, vecs=())]
return h_tsr.bind(vev_of_term)
def get_vev_agp(self,h_tsr: Tensor,):
"""Function to evaluate the expectation value of a normal
ordered tensor 'h_tsr' with respect to the projected BCS
or the AGP state. This can be done after translating the the
unitary group terms into the AGP basis algebra.
h_tsr = tensor whose VEV is to be evaluated
"""
transled = self._transl2agp(h_tsr)
transled = self._agp_dr.agp_simplify(transled,final_step=True)
res = self._agp_dr.get_vev(transled)
return Tensor(self, res.terms)
def extract_su2(self, expression: Tensor):
"""Bind function to map fermion strings to obvious SU2 (Pairing as well
as spin-flip operators)
"""
return expression.bind(self._extract_su2)
def canon_indices(self, expression: Tensor):
"""Bind function to canonicalize free / external indices.
"""
return expression.bind(
functools.partial(_canonicalize_indices, spec=self._spec))