# Landau levels in QCD

## TL;DR

This study provides the first lattice simulation evidence of Landau level structures in Dirac eigenmodes within full QCD under magnetic fields, revealing how these levels influence quark observables.

## Contribution

It introduces a novel lattice approach to identify and analyze Landau levels in four-dimensional QCD, connecting topological arguments with fermionic observable evaluations.

## Key findings

- Identification of lowest Landau level modes in lattice QCD
- Quantification of the lowest Landau level's contribution to quark condensate and spin polarization
- Potential for comparison with low-energy QCD models using Landau level approximation

## Abstract

We present first evidence for the Landau level structure of Dirac eigenmodes in full QCD for nonzero background magnetic fields, based on first principles lattice simulations using staggered quarks. Our approach involves the identification of the lowest Landau level modes in two dimensions, where topological arguments ensure a clear separation of these modes from energetically higher states, and an expansion of the full four-dimensional modes in the basis of these two-dimensional states. We evaluate various fermionic observables including the quark condensate and the spin polarization in this basis to find how much the lowest Landau level contributes to them. The results allow for a deeper insight into the dynamics of quarks and gluons in background magnetic fields and may be directly compared to low-energy models of QCD employing the lowest Landau level approximation.