Dynamical correlation functions of the mesoscopic pairing model

TL;DR

This paper provides exact calculations of dynamical correlation functions in the Richardson pairing model using Algebraic Bethe Ansatz, achieving high accuracy with simple two-particle states even in large systems.

Contribution

It introduces a method to compute correlation functions in the Richardson model with high precision, highlighting the sufficiency of two-particle states for accurate estimates.

Findings

Correlation functions estimated with over 99% sum-rule saturation.

Two-particle states are sufficient for accurate thermodynamic limit results.

Explicit results provided at half-filling and finite-size scaling discussed.

Abstract

We study the dynamical correlation functions of the Richardson pairing model (also known as the reduced or discrete-state BCS model) in the canonical ensemble. We use the Algebraic Bethe Ansatz formalism, which gives exact expressions for the form factors of the most important observables. By summing these form factors over a relevant set of states, we obtain very precise estimates of the correlation functions, as confirmed by global sum-rules (saturation above 99% in all cases considered). Unlike the case of many other Bethe Ansatz solvable theories, simple two-particle states are sufficient to achieve such saturations, even in the thermodynamic limit. We provide explicit results at half-filling, and discuss their finite-size scaling behavior.