Level crossings and Fisher information of two hard-core bosons in a two-dimensional trap

TL;DR

This paper provides an exact analytical solution for two hard-core bosons in a 2D harmonic trap, analyzing their energy spectrum, level crossings, and Fisher information to understand quantum correlations and localization.

Contribution

It offers the first exact solution for this system and links level crossings and Fisher information to quantum correlations in interacting particles.

Findings

Energy spectrum shows level crossings influenced by interaction range.

Fisher information reflects wavefunction localization and oscillatory behavior.

Localization properties relate to quantum correlations in the system.

Abstract

We investigate a two-body quantum system with hard-core interaction potential in a two-dimensional harmonic trap. We provide the exact analytical solution of the problem. The energy spectrum of this system as a function of the range of the interaction reveals level crossings which can be explained examining the potential and kinetic part of the energy, as well as the localization and oscillatory properties of the wavefunctions quantified by the Fisher information. The latter is sensitive to the wavefunction localization between nodes promoting this property as a resource of quantum correlations in interacting particle systems.