The Tamm-Dancoff Approximation as the boson limit of the Richardson-Gaudin equations for pairing

Abstract

A connection is made between the exact eigen states of the BCS Hamiltonian and the predictions made by the Tamm-Dancoff Approximation. This connection is made by means of a parametrised algebra, which gives the exact quasi-spin algebra in one limit of the parameter and the Heisenberg-Weyl algebra in the other. Using this algebra to construct the Bethe Ansatz solution of the BCS Hamiltonian, we obtain parametrised Richardson-Gaudin equations, leading to the secular equation of the Tamm-Dancoff Approximation in the bosonic limit. An example is discussed in depth.

Submitted to the proceedings of the Group28 conference (Newcastle-upon-Tyne, UK). Journal of Physics: Conference Series

References in corpus (1)

• Solving the Richardson equations close to the critical points

Cited by in corpus (2)

• Richardson-Gaudin integrability in the contraction limit of the quasispin
• The Dicke model as the contraction limit of a pseudo-deformed Richardson-Gaudin model