Approaching off-diagonal long-range order for 1+1-dimensional relativistic anyons

TL;DR

This paper constructs relativistic anyons in 1+1 dimensions, exploring their physical properties and how gauge coupling affects off-diagonal long-range order, revealing that gauge interactions destroy ODLRO despite anyonic statistics.

Contribution

It introduces models of relativistic anyons with density interactions and gauge coupling, analyzing their off-diagonal long-range order and effects of gauge invariance.

Findings

Anyonic statistics can approach ODLRO but is hindered by gauge coupling.

Gauge coupling induces a nonzero effective mass and screening.

Screening occurs independently of the anyonic statistics.

Abstract

We construct and study relativistic anyons in 1+1 dimensions generalizing well-known models of Dirac fermions. First, a model of free anyons is constructed and then extended in two ways: (i) by adding density-density interactions, as in the Luttinger model, and (ii) by coupling the free anyons to a U(1)-gauge field, as in the Schwinger model. Second, physical properties of these extensions are studied. By investigating off-diagonal long-range order (ODLRO) at zero temperature, we show that anyonic statistics allows one to get arbitrarily close to ODLRO but that this possibility is destroyed by the gauge coupling. The latter is due to a nonzero effective mass generated by gauge invariance, which we show also implies the presence of screening, independently of the anyonic statistics.