def opdm_to_ohdm_mapping(dim: int) -> DualBasis:
"""
Map the ck to kc
D1 + Q1 = I
Args:
dim: dimension of the spin-orbital basis
Returns:
DualBasis for the 1-RDM representability constraint
"""
dbe_list = []
for i in range(dim):
for j in range(i, dim):
dbe = DualBasisElement()
if i != j:
dbe.add_element('ck', (i, j), 0.5)
dbe.add_element('ck', (j, i), 0.5)
dbe.add_element('kc', (j, i), 0.5)
dbe.add_element('kc', (i, j), 0.5)
dbe.dual_scalar = 0.0
else:
dbe.add_element('ck', (i, j), 1.0)
dbe.add_element('kc', (i, j), 1.0)
dbe.dual_scalar = 1.0
# db += dbe
dbe_list.append(dbe)
return DualBasis(elements=dbe_list) # db
def d2q2element(p: int, q: int, r: int, s: int, factor: Union[float, int])\
-> DualBasisElement:
"""
Build the dual basis element for symmetric form of 2-marginal
:param p: tensor index
:param q: tensor index
:param r: tensor index
:param s: tensor index
:param factor: scaling coeff for a symmetric constraint
:return: the dual basis of the mapping
"""
dbe = DualBasisElement()
dbe.add_element('cckk', (p, q, r, s), -1.0 * factor)
dbe.add_element('kkcc', (r, s, p, q), +1.0 * factor)
if q == s:
dbe.add_element('ck', (p, r), factor)
if p == r:
dbe.add_element('ck', (q, s), factor)
if q == r:
dbe.add_element('ck', (p, s), -1. * factor)
if p == s:
dbe.add_element('ck', (q, r), -1. * factor)
dbe.dual_scalar = (
kronecker_delta(q, s) * kronecker_delta(p, r) -
kronecker_delta(q, r) * kronecker_delta(p, s)) * factor
return dbe
def nb_constraint(dim, nb):
"""
Constraint the trace of the alpha block of the opdm to equal the number
of spin-down electrons
Args:
dim: Dimension of the spin-orbital basis.
na: Number of spin down electrons
Returns:
DualBasis representing the cosntraint that is length 1
"""
dbe = DualBasisElement()
for i in range(dim // 2):
dbe.add_element('ck', (2 * i + 1, 2 * i + 1), 1.0)
dbe.dual_scalar = nb
return DualBasis(elements=[dbe])
def sz_constraint(dim: int, sz: Union[float, int]) -> DualBasis:
"""
Constraint on the 1-RDM
Args:
dim: dimension of the spin-orbital basis.
sz: expectation value of the magnetic quantum number.
Returns:
DualBasis
"""
dbe = DualBasisElement()
for i in range(dim // 2):
dbe.add_element('ck', (2 * i, 2 * i), 0.5)
dbe.add_element('ck', (2 * i + 1, 2 * i + 1), -0.5)
dbe.dual_scalar = sz
return DualBasis(elements=[dbe])
def na_constraint(dim: int, na: Union[float, int]) -> DualBasis:
"""
Constraint the trace of the alpha block of the opdm to equal the number
of spin-up electrons
Args:
dim: Dimension of the spin-orbital basis.
na: Number of spin up electrons
Returns:
DualBasis representing the cosntraint that is length 1
"""
dbe = DualBasisElement()
for i in range(dim // 2):
dbe.add_element('ck', (2 * i, 2 * i), 1.0)
dbe.dual_scalar = na
return DualBasis(elements=[dbe])
def g2d2map(p: int,
q: int,
r: int,
s: int,
factor: Optional[Union[float, int]] = 1) -> DualBasisElement:
"""
Build the dual basis element for a symmetric 2-marginal
:param p: tensor index
:param q: tensor index
:param r: tensor index
:param s: tensor index
:param factor: weighting of the element
:return: the dual basis element
"""
dbe = DualBasisElement()
if q == s:
dbe.add_element('ck', (p, r), -1. * factor)
dbe.add_element('ckck', (p, s, r, q), 1.0 * factor)
dbe.add_element('cckk', (p, q, r, s), 1.0 * factor)
dbe.dual_scalar = 0
return dbe