LAUSR

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 nontopological instantons using Monte Carlo methods on lattices of interacting spins. As a proof of principle, we systematically construct instanton solutions in $O(3)$ nonlinear 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 nontrivial field configurations in these theories. In particular, by means of simulated annealing, we demonstrate how to obtain domain walls, merons, and critical instanton solutions.