Phase transitions in a gas of anyons

TL;DR

This paper investigates phase transitions in a 3D lattice gas of loops with a topological term, revealing new effects of the Chern-Simons term on loop observables and phase behavior.

Contribution

It introduces a numerical study of a loop gas with a topological linking term, connecting it to the Abelian Higgs model and exploring the effects of the Chern-Simons term.

Findings

Phase transition persists as anyon mass decreases.

Chern-Simons term affects 't Hooft loop but not Wilson loop.

Both loops show perimeter law without massless particles.

Abstract

We continue our numerical Monte Carlo simulation of a gas of closed loops on a 3 dimensional lattice, however now in the presence of a topological term added to the action corresponding to the total linking number between the loops. We compute the linking number using certain notions from knot theory. Adding the topological term converts the particles into anyons. Using the correspondence that the model is an effective theory that describes the 2+1-dimensional Abelian Higgs model in the asymptotic strong coupling regime, the topological linking number simply corresponds to the addition to the action of the Chern-Simons term. We find the following new results. The system continues to exhibit a phase transition as a function of the anyon mass as it becomes small \cite{mnp}, although the phases do not change the manifestation of the symmetry. The Chern-Simons term has no effect on the Wilson loop, but it does affect the {\rm '}t Hooft loop. For a given configuration it adds the linking number of the 't Hooft loop with all of the dynamical vortex loops to the action. We find that both the Wilson loop and the 't Hooft loop exhibit a perimeter law even though there are no massless particles in the theory, which is unexpected.