Exactly-solvable models derived from a generalized Gaudin algebra

2004/07/16 by Gerardo Ortíz, G. Ortiz, Rolando D. Somma +3 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #cond-mat.str-el #cond-mat.supr-con #hep-th #nlin.SI #nucl-th

paper · pdf · doi:10.1016/j.nuclphysb.2004.11.008

published as Nucl.Phys. B707 (2005) 421-457

arxiv created 2004/07/16 · openalex publication_date 2004/12/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Abstract

We introduce a generalized Gaudin Lie algebra and a complete set of mutually commuting quantum invariants allowing the derivation of several families of exactly solvable Hamiltonians. Different Hamiltonians correspond to different representations of the generators of the algebra. The derived exactly-solvable generalized Gaudin models include the Bardeen-Cooper-Schrieffer, Suhl-Matthias-Walker, the Lipkin-Meshkov-Glick, generalized Dicke, the Nuclear Interacting Boson Model, a new exactly-solvable Kondo-like impurity model, and many more that have not been exploited in the physics literature yet.

Citations

• Validity of many-body approximation methods for a solvable model
• Theory of Superconductivity
• Exact study of the effect of level statistics in ultrasmall superconducting grains
• Bardeen-Cooper-Schrieffer Theory of Superconductivity in the Case of Overlapping Bands
• Ordering, metastability and phase transitions in two-dimensional systems
• Deconfined Quantum Critical Points
• Resistance Minimum in Dilute Magnetic Alloys
• MAXIMUM OCCUPATION NUMBER FOR COMPOSITE BOSON STATES
• Possible new effects in superconductive tunnelling

Cited by

• SU(3) Richardson–Gaudin models: three-level systems