Rotons in Anyon Superfluids

TL;DR

This paper calculates the excitation spectrum of a gas of nonrelativistic anyons with near-fermionic statistics, revealing a spectrum with Goldstone and roton-like massive branches, using bosonization techniques.

Contribution

It introduces a bosonization approach to analyze the excitation spectrum of anyon superfluids with specific statistical angles.

Findings

Spectrum includes Goldstone and massive roton-like branches.

Dispersion curves approach Landau levels at high momentum.

Method applies to large integer k statistical angles.

Abstract

We consider the problem of calculating the excitation spectrum of a gas of nonrelativistic anyons. When the anyons have statistics close to fermionic and the statistical angle has the form $\theta=\pi (1-\frac{1}{k})$ where $k$ is a large integer, the problem can be solved by employing the method of bosonization, which maps the problem to that of an infinite number of bosonic excitations coupled to a $U(1)$ Chern-Simons gauge field. The spectrum consists of a Goldstone boson branch and a large number of massive branches, each having roton minima and maxima. The dispersion curves asymptote to the Landau levels at large momentum.