Quantum phase transitions in Bose-Einstein condensates from a Bethe ansatz perspective

TL;DR

This paper explores quantum phase transitions in Bose-Einstein condensates by analyzing Bethe ansatz solutions, revealing a link between root behavior and phase changes, offering a new detection method.

Contribution

It introduces an approach connecting Bethe ansatz root structures to quantum phase transitions in Bose-Einstein condensates, providing an alternative detection technique.

Findings

Root behavior correlates with phase transitions

Bethe ansatz analysis detects quantum phase transitions

Method offers new insights into condensate models

Abstract

We investigate two solvable models for Bose-Einstein condensates and extract physical information by studying the structure of the solutions of their Bethe ansatz equations. A careful observation of these solutions for the ground state of both models, as we vary some parameters of the Hamiltonian, suggests a connection between the behavior of the roots of the Bethe ansatz equations and the physical behavior of the models. Then, by the use of standard techniques for approaching quantum phase transition - gap, entanglement and fidelity - we find that the change in the scenery in the roots of the Bethe ansatz equations is directly related to a quantum phase transition, thus providing an alternative method for its detection.