Enlarged Galilean symmetry of anyons and the Hall effect

TL;DR

This paper introduces an enlarged Galilean symmetry framework for non-relativistic anyons coupled to electromagnetic fields, explaining the anomalous Hall effect and extending to models of Bloch electrons.

Contribution

It develops a novel symmetry-based approach incorporating exotic central extension to describe anyons and their Hall motion behaviors.

Findings

Hall motions become mandatory at critical magnetic field values

The theory explains anomalous velocity relations in Hall effects

Extension to Bloch electrons provides a semiclassical effective model

Abstract

Enlarged planar Galilean symmetry, built of both space-time and field variables and also incorporating the ``exotic'' central extension is introduced. It is used to describe non-relativistic anyons coupled to an electromagnetic field. Our theory exhibits an anomalous velocity relation of the type used to explain the Anomalous Hall Effect. The Hall motions, characterized by a Casimir of the enlarged algebra, become mandatory for some critical value(s) of the magnetic field. The extension of our scheme yields the semiclassical effective model of the Bloch electron.