Integrability and exact solution for coupled BCS systems associated with the $su(4)$ Lie algebra

TL;DR

This paper presents an exactly solvable model for two coupled BCS systems based on the $su(4)$ algebra, providing explicit solutions for the energy spectrum and analyzing ground state properties at zero temperature.

Contribution

It introduces a new integrable model for coupled BCS systems linked to $su(4)$ and derives its exact solution using algebraic Bethe ansatz.

Findings

Exact energy spectrum obtained

Ground state energy and gap analyzed asymptotically

Correlation functions evaluated at zero temperature

Abstract

We introduce an integrable model for two coupled BCS systems through a solution of the Yang-Baxter equation associated with the Lie algebra $su(4)$. By employing the algebraic Bethe ansatz, we determine the exact solution for the energy spectrum. An asymptotic analysis is conducted to determine the leading terms in the ground state energy, the gap and some one point correlation functions at zero temperature.