Exact ground-state correlation functions of an atomic-molecular boson conversion model

TL;DR

This paper provides an exact analytical study of the ground-state properties and correlation functions of an atomic-molecular boson conversion model, revealing phase transitions and phase-specific correlations.

Contribution

It introduces an exact Bethe Ansatz solution for the model and derives explicit expressions for the ground-state energy and correlations, highlighting phase transition features.

Findings

Ground-state Bethe roots lie on the positive real-axis for certain parameters.

Derived an analytic expression for the ground-state energy.

Identified a line of quantum phase transitions separating molecular and mixed phases.

Abstract

We study the ground-state properties of an atomic-molecular boson conversion model through an exact Bethe Ansatz solution. For a certain range of parameter choices, we prove that the ground-state Bethe roots lie on the positive real-axis. We then use a continuum limit approach to obtain a singular integral equation characterising the distribution of these Bethe roots. Solving this equation leads to an analytic expression for the ground-state energy. The form of the expression is consistent with the existence of a line of quantum phase transitions, which has been identified in earlier studies. This line demarcates a molecular phase from a mixed phase. Certain correlation functions, which characterise these phases, are then obtained through the Hellmann-Feynman theorem.