On quantum phase crossovers in finite systems

Abstract

In this work we define a formal notion of a quantum phase crossover for certain Betheansatz solvable models. The approach we adopt exploits an exact mapping of thespectrum of a many-body integrable system, which admits an exact Bethe ansatzsolution, into the quasi-exactly solvable spectrum of a one-body Schrödinger operator.Bifurcations of the minima for the potential of the Schrödinger operator determinethe crossover couplings. By considering the behaviour of particular ground statecorrelation functions, these may be identified as quantum phase crossovers inthe many-body integrable system with finite particle number. In this approachthe existence of the quantum phase crossover is not dependent on the existenceof a thermodynamic limit, rendering applications to finite systems feasible. Westudy two examples of bosonic Hamiltonians which admit second-order crossovers.