Elliptic BCS-Richardson model and the modified algebraic Bethe ansatz

Abstract

We consider elliptic Gaudin-type model in an external magnetic field \cite{SkrPLA2005, SkrJGP2006, SkrJMP2006, SkrJPA2007, SkrNPB2019} associated with non-skew-symmetric elliptic r-matrix \cite{SkrPLA2005, SkrJGP2006, SkrJMP2006}. Using them we construct a new integrable fermion Hamiltonian of the Richardson type. We use the modified algebraic Bethe ansatz obtained for integrable models with the considered elliptic r-matrix in \cite{SkrNew} and find the spectrum of the obtained Richardson-type Hamiltonian in terms of solutions of the modified Bethe equations. The obtained results generalize our previous results on Richardson-type models \cite{SkrNPB2022}.

Supersymmetry and integrability for a class of XY central spin models

“…While the Bethe Ansatz approach described here does not yield expressions for the eigenstates, these are in principle accessible by adapting the algebraic Bethe Ansatz approach developed in [38][39][40] based on the quasi-classical Yang-Baxter equation. This appears to be a highly technical challenge.…”