Exactly Solvable BCS-BEC crossover Hamiltonians

TL;DR

This paper introduces a new method for deriving exactly solvable Hamiltonians in the BCS-BEC crossover, combining coordinate and algebraic Bethe ansatz techniques without needing transfer matrices.

Contribution

It presents a novel approach to identify exactly solvable Hamiltonians in the BCS-BEC crossover using Bethe ansatz methods without prior knowledge of transfer matrices.

Findings

Derived general exact solvability conditions for BCS-BEC Hamiltonians

Formulated eigenfunctions as factorisable operators on a reference state

Provided a framework for solving crossover Hamiltonians exactly

Abstract

We demonstrate a novel approach that allows the determination of very general classes of exactly solvable Hamiltonians via Bethe ansatz methods. This approach combines aspects of both the co-ordinate Bethe ansatz and algebraic Bethe ansatz. The eigenfunctions are formulated as factorisable operators acting on a suitable reference state. Yet, we require no prior knowledge of transfer matrices or conserved operators. By taking a variational form for the Hamiltonian and eigenstates we obtain general exact solvability conditions. 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).