Solutions of the Gaudin Equation and Gaudin Algebras

Abstract

Three well-known solutions of the Gaudin equation are obtained under a set of standard assumptions. By relaxing one of these assumptions we introduce a class of mutually commuting Hamiltonians based on a different solution of the Gaudin equation. Application of the algebraic Bethe ansatz technique to diagonalize these Hamiltonians reveals a new infinite dimensional complex Lie algebra.

arXiv comment15 pages of LATEX

References in corpus (4)

• Exactly solvable Richardson-Gaudin models for many-body quantum systems
• Exactly-Solvable Models Derived from a Generalized Gaudin Algebra
• An Exactly Solvable Model of Interacting Bosons
• Exactly Solvable Pairing Model Using an Extension of Richardson-Gaudin Approach

Cited by in corpus (5)

• Onset of many-body quantum chaos due to breaking integrability
• Integrable and chaotic dynamics of spins coupled to an optical cavity
• Solution of the classical Yang--Baxter equation with an exotic symmetry, and integrability of a multi-species boson tunneling model
• Quadratic operator relations and Bethe equations for spin-1/2 Richardson-Gaudin models
• Symmetry and Supersymmetry in Nuclear Pairing: Exact Solutions