def _get_fermi_partitions(term: Term, spec: _AGPFSpec):
"""Given a term with a list of fermionic vectors, extract the various
partitions of N, Pdag and P kind of terms.
Assumes: All possible simplification and Pairing / SU2 extraction
has been performed, i.e. all the indices are distinct.
"""
vecs = term.vecs
amp = term.amp
fermi_indcs = []
cr = spec.c_dag.base
an = spec.c_.base
# First extract all the indices of fermion operators
for v in vecs:
if v.base in (cr, an):
fermi_indcs.append(v.indices[1])
if len(fermi_indcs) == 0:
# if there are no fermion operators, return the term as it is
return [Term(sums=term.sums, amp=amp, vecs=vecs)]
else:
# if there are fermion operators, then get all the possible
# partitions of indices
deltas_partns = list(_generate_partitions(fermi_indcs))
# get a list of even partitions, i.e. throw away partitions involving
# odd number of indices
evens = [
all(
len(deltas_partns[i][j]) % 2 == 0
for j in range(len(deltas_partns[i])))
for i in range(len(deltas_partns))
]
# Now iterate through the list of partitions and form the deltas expression
# for the amplitude
delta_amp = Integer(0)
for i in range(len(deltas_partns)):
# if statement for even partitions
if evens[i]:
pt = deltas_partns[i]
else:
continue
# Form the delta expressions
delta_intmd = Integer(1)
for i in range(len(pt)):
delta_intmd *= _construct_deltas(pt[i])
if i > 0:
delta_intmd *= (1 - KroneckerDelta(pt[i][0], pt[i - 1][0]))
delta_amp += delta_intmd
new_amp = amp * delta_amp
return [Term(sums=term.sums, amp=new_amp, vecs=vecs)]
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=())]
def _isAGP(self, term):
"""Returns True if the vectors in the term are generators of the AGP algebra, otherwise False"""
vecs = term.vecs
for v in vecs:
if v.base not in (self.cartan, self.raise_, self.lower):
raise ValueError('Unexpected generator of the AGP Algebra', v)
return [Term(sums=term.sums, amp=term.amp, vecs=term.vecs)]
def _isUGA(self,term):
"""Function returns True if the vectors are uga generators, otherwise False"""
vecs = term.vecs
for v in vecs:
if v.base!=self.uga:
raise ValueError('Unexpected generator of the Unitary Group',v)
return [Term(sums=term.sums, amp=term.amp, vecs=term.vecs)]
def _subst_actv_vec_rdm (term: Term, rdm: IndexedBase, actv_range, op_parser, resolvers):
parsed = [op_parser (vec, term) for vec in term.vecs]
ranges = [try_resolve_range (p[2][0], dict(term.sums), resolvers.value) for p in parsed]
inac_vecs = [vec for r, vec in zip (ranges, term.vecs) if not r==actv_range]
actv_parsed = [p for r, p in zip (ranges, parsed) if r==actv_range]
amp = term.amp
if len (actv_parsed) > 0:
actv_cr_idxs = sum([[p[2][0]] for p in actv_parsed if p[1]==CR], [])
actv_an_idxs = sum([[p[2][0]] for p in reversed (actv_parsed) if p[1]==AN], [])
actv_idxs = actv_cr_idxs + actv_an_idxs
amp = amp * rdm[actv_idxs]
return Term (term.sums, amp, inac_vecs)
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=())]
def _canonicalize_indices(term: Term, spec: _AGPFSpec):
"""Here, we canonicalize the free indices in the tensor expressions - that
is replace the higher key indices with lower key ones everywhere
"""
# get the new term and substs
new_amp, substs = _try_simpl_unresolved_deltas(term.amp)
# check for overlap in the dlists and unique_indices
# if any of the maps contain two indices that are supposed to be unique,
# it should return zero/empty term.
unique_list = spec.unique_ind
# New substitutions based on the chain of delta
new_substs = {}
if substs:
dlists = _delta_map(substs)
for s1 in dlists:
s1_sorted = list(ordered(s1))
j = 1
while j < len(s1_sorted):
new_substs[s1_sorted[j]] = s1_sorted[0]
j += 1
if not unique_list:
continue
for s2 in unique_list:
if len(list(s1 & s2)) > 1:
return []
else:
continue
# construct the new term
new_term = term.subst(new_substs)
return [Term(sums=new_term.sums, amp=new_amp, vecs=new_term.vecs)]
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=())]
def _get_su2_vecs(term: Term, spec: _AGPFSpec):
"""Given a term with a list of vectors, extract the obvious BCS vectors
NOTE: This bind function assumes that the term has already been simplified
NOTE2: We just ignore the SP and SM terms in extracting su2
"""
vecs = term.vecs
amp = term.amp
int_vecs = []
new_vecs = []
Pdag = spec.Pdag
P = spec.P
N = spec.N
N_up = spec.Nup
N_dn = spec.Ndn
SP = spec.S_p
SM = spec.S_m
SZ = spec.S_z
cr = (spec.c_dag.base, spec.c_dag.indices[0])
an = (spec.c_.base, spec.c_.indices[0])
# Get rid of the trivial case where no SU2 vector is possible.
if len(vecs) <= 1:
new_vecs = vecs
return [Term(sums=term.sums, amp=amp, vecs=new_vecs)]
# Now onto the more involved situations:
# First, let us extract all the number and pair-annihilation operators
i = 0
while i < (len(vecs) - 1):
v1 = (vecs[i].base, vecs[i].indices[0])
v2 = (vecs[i + 1].base, vecs[i + 1].indices[0])
if (v1 == cr):
if (v2 == an):
if (vecs[i].indices[1:] == vecs[i + 1].indices[1:]):
if vecs[i].indices[2] == SpinOneHalf.UP:
int_vecs.append(N_up[vecs[i].indices[1]])
elif vecs[i].indices[2] == SpinOneHalf.DOWN:
int_vecs.append(N_dn[vecs[i].indices[1]])
i += 2
continue
# elif (vecs[i].indices[1] == vecs[i+1].indices[1]):
# if vecs[i].indices[2] == SpinOneHalf.UP:
# int_vecs.append(SP[vecs[i].indices[1]])
# i += 2
# continue
# else:
# int_vecs.append(SM[vecs[i].indices[1]])
# i += 2
# continue
else:
int_vecs.append(vecs[i])
i += 1
continue
elif (v2 == cr):
# Do not consider the pair-creation operators yet
int_vecs.append(vecs[i])
i += 1
continue
else:
raise ValueError('Input term is not simplified')
elif (v1 == an):
if (v2 == an):
if (vecs[i].indices[1] == vecs[i + 1].indices[1]):
# if both annihilation, and have same lattice index,
# then assuming the term is simplified, the spins
# must be opposite (first one would be DOWN)
int_vecs.append(P[vecs[i].indices[1]])
i += 2
continue
else:
int_vecs.append(vecs[i])
i += 1
continue
else:
int_vecs.append(vecs[i])
i += 1
continue
else:
int_vecs.append(vecs[i])
i += 1
continue
# If the last two operators did not map, we are left with
# the last fermion operator
if i == len(vecs) - 1:
int_vecs.append(vecs[i])
# Now map all the pair-creation operators
i = 0
while i < (len(int_vecs) - 1):
v1 = (int_vecs[i].base, int_vecs[i].indices[0])
v2 = (int_vecs[i + 1].base, int_vecs[i + 1].indices[0])
if (v1 == cr):
if (v2 == cr):
if (int_vecs[i].indices[1] == int_vecs[i + 1].indices[1]):
# if both creation, and have same lattice index,
# then assuming term is simplified, the spins must be
# opposite.
new_vecs.append(Pdag[int_vecs[i].indices[1]])
i += 2
continue
else:
new_vecs.append(int_vecs[i])
i += 1
continue
else:
new_vecs.append(int_vecs[i])
i += 1
continue
# raise ValueError('Input term is not simplified')
else:
new_vecs.append(int_vecs[i])
i += 1
continue
# If the last two operators did not map, we are left with
# the last fermion operator
if i == len(int_vecs) - 1:
new_vecs.append(int_vecs[i])
return [Term(sums=term.sums, amp=amp, vecs=new_vecs)]