Exact mesoscopic correlation functions of the pairing model

TL;DR

This paper derives exact expressions for static correlation functions in the Richardson pairing model using Algebraic Bethe Ansatz, enabling numerical evaluation for large systems and analyzing finite-size effects.

Contribution

It provides the first exact, numerically accessible formulas for correlation functions in the Richardson pairing model using Algebraic Bethe Ansatz.

Findings

Explicit correlation functions at half-filling

Numerical evaluation for large particle numbers

Finite-size scaling analysis

Abstract

We study the static correlation functions of the Richardson pairing model (also known as the reduced or discrete-state BCS model) in the canonical ensemble. Making use of the Algebraic Bethe Ansatz formalism, we obtain exact expressions which are easily evaluated numerically for any value of the pairing strength up to large numbers of particles. We provide explicit results at half-filling and extensively discuss their finite-size scaling behavior.