Renormalization group analysis of resonantly interacting anyons

TL;DR

This paper develops a field theory for resonantly interacting anyons, revealing a limit cycle in four-body interactions that suggests an infinite spectrum of bound states, advancing understanding of anyonic quantum systems.

Contribution

It introduces a perturbative field theory for anyons near the fermionic limit and uncovers a novel limit cycle behavior in four-body couplings.

Findings

Identifies two fixed points in the renormalization group flow.

Discovers a limit cycle in four-body interactions.

Predicts an infinite set of four-anyon bound states.

Abstract

We formulate a field theory for resonantly interacting anyons, that enables us to perform a perturbative calculation near the fermionic limit. We derive renormalization group equations for three-body and four-body couplings at one-loop order. In addition to two fixed points, we find a limit cycle behavior in the four-body coupling, which implies an infinite set of bound states in the four-anyon system.