Exact results for persistent currents of two bosons in a ring lattice

TL;DR

This paper provides exact solutions for the ground state and persistent currents of two interacting bosons in a ring lattice with synthetic flux, revealing how interactions influence current periodicity and correlations.

Contribution

It offers the first exact analysis of two bosons in a lattice ring with flux, showing the coupling of center of mass and relative motion and fractional flux quantum in attractive interactions.

Findings

Persistent current periodicity remains standard for repulsive bosons.

Attractive interactions lead to fractionalized flux quantum.

Density after expansion can experimentally reveal persistent currents.

Abstract

We study the ground state of two interacting bosonic particles confined in a ring-shaped lattice potential and subjected to a synthetic magnetic flux. The system is described by the Bose-Hubbard model and solved exactly through a plane-wave Ansatz of the wave function. We obtain energies and correlation functions of the system both for repulsive and attractive interactions. In contrast with the one-dimensional continuous theory described by the Lieb-Liniger model, in the lattice case we prove that the center of mass of the two particles is coupled with its relative coordinate. Distinctive features clearly emerge in the persistent current of the system. While for repulsive bosons the persistent current displays a periodicity given by the standard flux quantum for any interaction strength, in the attractive case the flux quantum becomes fractionalized in a manner that depends on the interaction. We also study the density after the long time expansion of the system which provides an experimentally accessible route to detect persistent currents in cold atom settings. Our results can be used to benchmark approximate schemes for the many-body problem.