Full 2D Numerical Study of the Quantum Hall Skyrme Crystal

TL;DR

This paper presents the first comprehensive 2D numerical analysis of quantum Hall Skyrmion crystals, revealing their structure, stability, and preferred lattice configuration using advanced simulation techniques.

Contribution

It introduces a full 2D numerical study of quantum Hall Skyrmions and their crystal formations, overcoming previous approximation limitations.

Findings

Only charge-one and charge-two Skyrmions are bound.

The Skyrme crystal likely forms a triangular lattice of charge-two Skyrmions.

Provides new insights into Skyrmion deformation and symmetry in quantum Hall systems.

Abstract

Spin textures arise in the effective action approach to the quantum Hall effect. Up to now these textures, also called Skyrmions, have been mainly studied using approximations. Studies of its finite density form, the crystal, have been limited to a given symmetry and tend ignore Skyrmion deformation. Using a simulated annealing technique, adapted to problems with a long-range interaction, we are able to present the first full 2D study of quantum Hall Skyrmions and the corresponding crystals. Our results show that only the Skyrmions with topological charge one and two are bound and that the Skyrme crystal is probably a triangular lattice made of charge-two Skyrmions.