Exactly-Solvable Models Derived from a Generalized Gaudin Algebra

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.

References in corpus (6)

• "Deconfined" quantum critical points
• Nature and Measure of Entanglement in Quantum Phase Transitions
• Exactly-solvable models for atom-molecule hamiltonians
• Solving the Richardson equations for Fermions
• Quasi-classical descendants of disordered vertex models with boundaries
• Interplay between pairing and exchange in small metallic dots

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