Bosonic continuum theory of one-dimensional lattice anyons

TL;DR

This paper derives a continuum theory for 1D lattice anyons using interacting bosons, preserving exchange phase periodicity and connecting experimental lattice anyons with continuum models, including Kundu anyons.

Contribution

It introduces a new continuum limit for 1D lattice anyons that maintains exchange phase periodicity and links lattice models with continuum theories.

Findings

Numerical estimation of the Luttinger parameter as a function of exchange angle.

Prediction of different velocities for left- and right-moving excitations.

Establishment of a mapping between lattice anyons and continuum theories.

Abstract

Anyons with arbitrary exchange phases exist on 1D lattices in ultracold gases. Yet, known continuum theories in 1D do not match. We derive the continuum limit of 1D lattice anyons via interacting bosons. The theory maintains the exchange phase periodicity fully analogous to 2D anyons. This provides a mapping between experiments, lattice anyons, and continuum theories, including Kundu anyons with a natural regularization as a special case. We numerically estimate the Luttinger parameter as a function of the exchange angle to characterize long-range signatures of the theory and predict different velocities for left- and right-moving collective excitations.