Quadratic operator relations and Bethe equations for spin-1/2 Richardson–Gaudin models. (2nd July 2018)

• Record Type: Journal Article
• Authors: Dimo, Claude; Faribault, Alexandre
• Is Part Of: Journal of physics. Volume 51:Number 32(2018)
• Publication Date: 2018-07-02
• Subjects: XYZ models -- quantum integrable models -- Richardson–Gaudin models; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aaccb4
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: In this work we demonstrate how one can, in a generic approach, derive a set of N simple quadratic Bethe equations for integrable Richardson–Gaudin (RG) models built out of N spins-1/2. These equations depend only on the N eigenvalues of the various conserved charges so that any solution of these equations defines, indirectly through the corresponding set of eigenvalues, one particular eigenstate. The proposed construction covers the full class of integrable RG models of the XYZ (including the subclasses of XXZ and XXX models) type realised in terms of spins-1/2, coupled with one another through, , terms, including, as well, magnetic field-like terms linear in the Pauli matrices. The approach exclusively requires integrability, defined here only by the requirement that N conserved charges R i (with ) such that exist. The result is therefore valid, and equally simple, for models with or without symmetry, with or without a properly defined pseudo-vacuum as well as for models with non-skew symmetric couplings.