Confinement-deconfinement transitions for two-dimensional Dirac particles

TL;DR

This paper characterizes the spectral properties of a 2D massless Dirac operator influenced by magnetic and electric fields, identifying conditions for discrete and dense spectrum based on field behavior at infinity.

Contribution

It provides a sharp criterion linking magnetic and electric field behaviors at infinity to the spectrum of the Dirac operator, advancing understanding of spectral transitions.

Findings

Derived a criterion for spectrum discreteness

Identified conditions for dense pure point spectrum

Linked spectral properties to asymptotic behavior of fields

Abstract

We consider a two-dimensional massless Dirac operator coupled to a magnetic field $B$ and an electric potential $V$ growing at infinity. We find a characterization of the spectrum of the resulting operator $H$ in terms of the relation between $B$ and $V$ at infinity. In particular, we give a sharp condition for the discreteness of the spectrum of $H$ beyond which we find dense pure point spectrum.