Elliptic BCS-Richardson model and the modified algebraic Bethe ansatz

Abstract

Abstract We consider the elliptic Gaudin-type model in an external magnetic field (Skrypnyk T 2005 Phys. Lett. A 334 390–9; Skrypnyk T 2005 Phys. Lett. A 347 266–7; Skrypnyk T 2006 J. Geom. Phys. 57 53–67; Skrypnyk T 2006 J. Math. Phys. 47; Skrypnyk T 2007 J. Phys. A 40 1611–23; Skrypnyk T 2019 Nucl. Phys. B 941 225–48) associated with non-skew-symmetric elliptic r-matrix (Skrypnyk T 2005 Phys. Lett. A 334 390–9; Skrypnyk T 2005 Phys. Lett. A 347 266–7; Skrypnyk T 2006 J. Geom. Phys. 57 53–67; Skrypnyk T 2006 J. Math. Phys. 47). 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 (Skrypnyk T 2023 Nucl. Phys. B 988 116102) 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 (Skrypnyk T 2022 Nucl. Phys. B 975 115679).