Irrational vs. rational charge and statistics in two-dimensional quantum systems

TL;DR

This paper demonstrates the existence of quasiparticle excitations with irrational charge and statistics in 2D quantum systems, revealing their re-rationalization under certain conditions and implications for quantum statistics.

Contribution

It introduces the concept of irrational charge and statistics in 2D quantum systems and analyzes their behavior within the Dirac equation framework.

Findings

Existence of irrational charge and statistics quasiparticles

Charge re-rationalizes to 1/2 at zero temperature

Exchange statistics become that of quartons (half-semions)

Abstract

We show that quasiparticle excitations with irrational charge and irrational exchange statistics exist in tight-biding systems described, in the continuum approximation, by the Dirac equation in (2+1)-dimensional space and time. These excitations can be deconfined at zero temperature, but when they are, the charge re-rationalizes to the value 1/2 and the exchange statistics to that of "quartons" (half-semions).