Stable Topological Skyrmions on the 2D Lattice

TL;DR

This paper introduces a lattice modification of the 2D Heisenberg model to stabilize topological solitons, known as skyrmions, on a discrete lattice, extending continuum topological models.

Contribution

It proposes a novel lattice formulation that stabilizes topological skyrmions, bridging continuum models and discrete lattice implementations.

Findings

Stable topological skyrmions achieved on the 2D lattice

Lattice modifications preserve topological properties

Potential for numerical simulations of skyrmions

Abstract

In the continuum O(3) sigma model in two spatial dimensions, there are topological solitons whose size can be stabilized by adding Skyrme and potential terms. This paper describes a lattice version, namely a natural way of modifying the 2d Heisenberg model to achieve topological stability on the lattice.