Landau Levels in Lattice QCD

TL;DR

This paper explores how Landau levels manifest in lattice QCD, focusing on defining the lowest Landau level and assessing its approximation of physical quantities despite lattice discretization effects.

Contribution

It introduces a method to define the lowest Landau level in lattice QCD and evaluates its effectiveness in approximating physical observables.

Findings

The lowest Landau level remains distinguishable despite lattice artifacts.

Physical quantities can be approximated using only the lowest Landau level.

Discretization effects spread out Landau levels but do not eliminate their core structure.

Abstract

The spectrum of the two-dimensional continuum Dirac operator in the presence of a uniform background magnetic field consists of Landau levels, which are degenerate and separated by gaps. On the lattice the Landau levels are spread out by discretization artefacts, but a remnant of their structure is clearly visible (Hofstadter butterfly). If one switches on a non-Abelian interaction, the butterfly structure will be smeared out, but the lowest Landau level (LLL) will still be separated by a gap from the rest of the spectrum. In this talk we discuss how one can define the LLL in QCD and check how well certain physical quantities are approximated by taking into account only the LLL.