Spontaneous Symmetry Breaking in the Non-Abelian Anyon Fluid

TL;DR

This paper investigates a non-Abelian anyon fluid in (2+1) dimensions, revealing a superfluid phase with spontaneous symmetry breaking and identifying both massless and massive excitations.

Contribution

It extends the mean field approach to non-Abelian anyons, demonstrating a superfluid phase and analyzing the excitation spectrum in this context.

Findings

Discovery of a superfluid phase in non-Abelian anyon systems

Identification of Goldstone and massive modes in the excitation spectrum

Smooth connection between non-Abelian and Abelian superfluid phases

Abstract

We study the theory of non-relativistic matter with non-Abelian $U(2)$ Chern-Simons gauge interaction in $(2+1)$ dimensions. We adopt the mean field approximation in the current-algebra formulation already applied to the Abelian anyons. We first show that this method is able to describe both ``boson-based'' and ``fermion-based'' anyons and yields consistent results over the whole range of fractional statistics. In the non-Abelian theory, we find a superfluid (and superconductive) phase, which is smoothly connected with the Abelian superfluid phase originally discovered by Laughlin. The characteristic massless excitation is the Goldstone particle of the specific mechanism of spontaneous symmetry breaking. An additional massive mode is found by diagonalizing the non-Abelian, non-local, Hamiltonian in the radial gauge.