Block-diagonalization of pairing Hamiltonians using spin transpositions

Abstract

Using two-electron spin transpositions within BCS pairs, it is shown that an efficient block-diagonal decomposition of the Hamiltonian matrices associated with general pairing models is possible. The ratio of the dimension of the full Hilbert space to the size of the largest submatrix obtained grows exponentially with the number of electron pairs. This remarkable result holds for any electron filling. The approach is exemplified on the usual BCS model.