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arXiv · 1511.03127

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

Alexandre Faribault·Hugo Tschirhart·Nicolas Muller
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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.

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Alexandre Faribault, Hugo Tschirhart, Nicolas Muller. 2015-11-10. Determinant representation of the domain-wall boundary condition partition function of a Richardson-Gaudin model containing one arbitrary spin. https://doi.org/10.1088/1751-8113%2F49%2F18%2F185202

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