Thermodynamics of dilute anyon gases from fusion constraints

TL;DR

This paper develops a universal statistical mechanics framework for dilute anyon gases, enabling the calculation of thermodynamic properties using fusion and braiding data, relevant for understanding 2D quantum materials.

Contribution

It introduces a general theory for the thermodynamics of dilute anyon gases based on fusion constraints and universal braiding data, unifying various models.

Findings

Constructed a distribution function for dilute anyon gases.

Derived thermodynamic observables from fusion and braiding data.

Unified different models of itinerant anyons under a common framework.

Abstract

Recent measurements on 2d materials tuning between fractional quantum anomalous Hall phases and a plethora of correlated electronic states call for a detailed understanding of the dynamics of anyons. Here we develop a general theory of the statistical mechanics of anyon gases at finite temperature, valid in regimes where the anyons are sufficiently dilute and can be treated as weakly interacting particles. We find that with a minimal set of universal braiding and fusion data, along with information about the hierarchy of anyon gaps, it is possible to construct a distribution function for any dilute anyon gas, as well as derive thermodynamic observables. Our results are built on an anyon exclusion principle manifesting as a constraint on fusion outcomes of physical states. Our approach unifies and streamlines a range of results for itinerant anyon models, from solvable lattice Hamiltonians to large-N field theories.