Determinant representation of the domain-wall boundary condition partition function of a Richardson-Gaudin model containing one arbitrary spin

TL;DR

This paper derives a determinant formula for the partition function of a specific Richardson-Gaudin model with one large spin and multiple spin-1/2 particles, simplifying numerical computations.

Contribution

It introduces a new determinant representation for the partition function involving an arbitrary large spin in Richardson-Gaudin models, facilitating easier numerical solutions.

Findings

Provides a determinant expression for the partition function.

Enables more stable and faster numerical computations.

Applicable to models with one large spin and multiple spin-1/2 particles.

Abstract

In this work we present a determinant expression for the domain-wall boundary condition partition function of rational (XXX) Richardson-Gaudin models which, in addition to $N-1$ spins $\frac{1}{2}$, contains one arbitrarily large spin $S$. The proposed determinant representation is written in terms of a set of variables which, from previous work, are known to define eigenstates of the quantum integrable models belonging to this class as solutions to quadratic Bethe equations. Such a determinant can be useful numerically since systems of quadratic equations are much simpler to solve than the usual highly non-linear Bethe equations. It can therefore offer significant gains in stability and computation speed.