double_commutator

double_commutator(op_a, op_b, op_c, sign=False)

Compute symmetric double commutator of op_a, op_b and op_c.

See also Equation (13.6.18) in [1]. If sign is False, it returns

\[[[A, B], C]/2 + [A, [B, C]]/2 = (2ABC + 2CBA - BAC - CAB - ACB - BCA)/2.\]

If sign is True, it returns

\[\lbrace[A, B], C\rbrace/2 + \lbrace A, [B, C]\rbrace/2 = (2ABC - 2CBA - BAC + CAB - ACB + BCA)/2.\]

Parameters:

• op_a (SparseLabelOp) – Operator A.

• op_b (SparseLabelOp) – Operator B.

• op_c (SparseLabelOp) – Operator C.

• sign (bool) – False anti-commutes, True commutes.

Returns:

The computed double commutator.

Return type:

SparseLabelOp

References

[1]: R. McWeeny.

Methods of Molecular Quantum Mechanics. 2nd Edition, Academic Press, 1992. ISBN 0-12-486552-6.