Observing instantons directly on the lattice without cooling

TL;DR

This paper introduces a new lattice method for directly observing instantons in the Abelian Higgs model by measuring topological charge over larger regions, effectively reducing ultraviolet noise.

Contribution

The paper presents a novel approach to identify and localize instantons on the lattice without cooling, enabling direct measurement of instanton size and density.

Findings

Effective instanton detection without cooling.

Ability to measure instanton size and probability density.

Reinterpretation of local dislocations as boundary condition effects.

Abstract

Based on the study of the simple Abelian Higgs model in $1+1$ dimensions we will present a new method to identify and localize extended instantons. The idea is to measure the topological charge on regions somewhat larger than the extended instantons so as to average out the ultraviolet fluctuations but without losing the detailed topological information when going to the full space. The instanton size and probability density can be directly extracted from this analysis. Local dislocations, which can be avoided for fine enough lattices, can be reinterpreted as modified boundary conditions producing sectors with net topological charge.