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

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.

17 pages, 0 figures

References in corpus (7)

• Gaudin models solver based on the Bethe ansatz/ordinary differential equations correspondence
• Integrability-based analysis of the hyperfine-interaction -nduced decoherence in quantum dots
• An eigenvalue-based method and determinant representations for general integrable XXZ Richardson-Gaudin models
• On the determinant representations of Gaudin models' scalar products and form factors
• Non-equilibrum dynamics in the strongly excited inhomogeneous Dicke model
• Eigenvalue-based determinants for scalar products and form factors in Richardson-Gaudin integrable models coupled to a bosonic mode
• Algebraic Bethe Ansätze and eigenvalue-based determinants for Dicke-Jaynes-Cummings-Gaudin quantum integrable models

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• Steady-states of out-of-equlibrium inhomogeneous Richardson-Gaudin quantum integrable models in quantum optics