Exact correlation functions of the BCS model in the canonical ensemble

Abstract

We evaluate correlation functions of the BCS model for finite number of particles. The integrability of the Hamiltonian relates it with the Gaudin algebra $\mathcal{G}[sl(2)]$. Therefore, a theorem that Sklyanin proved for the Gaudin model, can be applied. Several diagonal and off-diagonal correlators are calculated. The finite size scaling behavior of the pairing correlation function is studied.

Comments: 4 pages revtex; 2 figures .eps. Revised version to be published in Phys. Rev. Lett