One-dimensional anyons with competing $\delta$-function and derivative $\delta$-function potentials

TL;DR

This paper introduces an exactly solvable one-dimensional anyon model with both delta-function and derivative delta-function interactions, revealing richer physics and unique signatures related to particle velocities and interactions.

Contribution

It develops a generalized exactly solvable anyon model with competing interactions, extending previous models and uncovering new physical insights.

Findings

Rich physics beyond standard delta-function anyon models

Anyonic signatures linked to particle velocities and interactions

Exact Bethe ansatz solutions derived for the model

Abstract

We propose an exactly solvable model of one-dimensional anyons with competing $\delta$-function and derivative $\delta$-function interaction potentials. The Bethe ansatz equations are derived in terms of the $N$-particle sector for the quantum anyonic field model of the generalized derivative nonlinear Schr\"{o}dinger equation. This more general anyon model exhibits richer physics than that of the recently studied one-dimensional model of $\delta$-function interacting anyons. We show that the anyonic signature is inextricably related to the velocities of the colliding particles and the pairwise dynamical interaction between particles.