Exploring instantons with spin-lattice systems

TL;DR

This paper demonstrates how Monte Carlo methods on spin-lattice systems can effectively construct and analyze instanton solutions, including topological configurations like domain walls and merons, in models relevant to high energy and condensed matter physics.

Contribution

It introduces a novel approach using Monte Carlo simulations on spin-lattice systems to study instantons in non-linear sigma models with Dzyaloshinskii-Moriya interactions.

Findings

Successfully constructed instanton solutions in 1+1 and 1+2 dimensions.

Demonstrated the effectiveness of Monte Carlo methods in identifying topological configurations.

Showed the correspondence between spin-lattice models and field theory instantons.

Abstract

Instanton processes are present in a variety of quantum field theories relevant to high energy as well as condensed matter physics. While they have led to important theoretical insights and physical applications, their underlying features often remain elusive due to the complicated computational treatment. Here, we address this problem by studying topological as well as non-topological instantons using Monte Carlo methods on lattices of interacting spins. As a proof of principle, we systematically construct instanton solutions in $O(3)$ non-linear sigma models with a Dzyaloshinskii-Moriya interaction in $(1 + 1)$ and $(1 + 2)$ dimensions, thereby resembling an example of a chiral magnet. We demonstrate that, due to their close correspondence, Monte Carlo techniques in spin-lattice systems are well suited to describe topologically non-trivial field configurations in these theories. In particular, by means of simulated annealing, we demonstrate how to obtain domain walls, merons and critical instanton solutions.