A variational approach for the Quantum Inverse Scattering Method

TL;DR

This paper presents a variational method to solve certain Hamiltonians exactly using Bethe ansatz, applicable to models describing superconductivity and Bose-Einstein condensation without prior integrability knowledge.

Contribution

It introduces a novel variational approach for the Quantum Inverse Scattering Method that does not depend on known conserved operators, broadening the scope of exactly solvable models.

Findings

Derives general exact solvability conditions for Hamiltonians with Cooper pairs and bosonic modes.

Identifies seven subcases of previously known models within the framework.

Provides a unified variational framework applicable to BCS-BEC crossover models.

Abstract

We introduce a variational approach for the Quantum Inverse Scattering Method to exactly solve a class of Hamiltonians via Bethe ansatz methods. We undertake this in a manner which does not rely on any prior knowledge of integrability through the existence of a set of conserved operators. The procedure is conducted in the framework of Hamiltonians describing the crossover between the low-temperature phenomena of superconductivity, in the Bardeen-Cooper-Schrieffer (BCS) theory, and Bose-Einstein condensation (BEC). The Hamiltonians considered describe systems with interacting Cooper pairs and a bosonic degree of freedom. We obtain general exact solvability requirements which include seven subcases which have previously appeared in the literature.