Exactly-Solvable Models Derived from a Generalized Gaudin Algebra

TL;DR

This paper introduces a generalized Gaudin algebra framework that enables the derivation of numerous exactly solvable quantum models, expanding the toolkit for analyzing complex many-body systems.

Contribution

It presents a new algebraic structure that unifies and generalizes existing exactly solvable models, including several well-known and novel Hamiltonians.

Findings

Derived multiple exactly solvable Hamiltonians from the generalized algebra.

Unified framework encompasses models like BCS, Lipkin-Meshkov-Glick, and new impurity models.

Expanded the set of exactly solvable models in quantum many-body physics.

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.