Mott Transition in An Anyon Gas

TL;DR

This paper introduces a lattice model of anyons that exhibits a Mott insulator to quantum Hall fluid transition, revealing how critical properties vary continuously with anyon statistics and connecting to quantum Hall and superconductor-insulator experiments.

Contribution

The study presents a novel lattice model of anyons with a variable statistics parameter, analyzing the critical behavior of the Mott transition across different anyon types.

Findings

Critical properties depend on anyon statistics due to gauge fluctuations.

The model exhibits a fixed line of critical points with continuously varying universality classes.

Connections to fractional quantum Hall transitions and superconductor-insulator transitions are discussed.

Abstract

We introduce and analyze a lattice model of anyons in a periodic potential and an external magnetic field which exhibits a transition from a Mott insulator to a quantum Hall fluid. The transition is characterized by the anyon statistics, $\alpha$, which can vary between Fermions, $\alpha=0$, and Bosons, $\alpha=1$. For bosons the transition is in the universality class of the classical three-dimensional XY model. Near the Fermion limit, the transition is described by a massless $2+1$ Dirac theory coupled to a Chern-Simons gauge field. Analytic calculations perturbative in $\alpha$, and also a large N-expansion, show that due to gauge fluctuations, the critical properties of the transition are dependent on the anyon statistics. Comparison with previous calcualations at and near the Boson limit, strongly suggest that our lattice model exhibits a fixed line of critical points, with universal critical properties which vary continuosly and monotonically as one passes from Fermions to Bosons. Possible relevance to experiments on the transitions between plateaus in the fractional quantum Hall effect and the magnetic field-tuned superconductor-insulator transition are briefly discussed.