Mass of quantum topological excitations and order parameter finite size dependence

TL;DR

This paper investigates the behavior of topological excitations in the $O(n)$ vector model, showing that their mass diverges in higher dimensions, which impacts finite size effects and order parameter behavior.

Contribution

It provides a theoretical analysis linking the divergence of topological excitation mass to the dimensionality in the $O(n)$ model, supported by comparison with numerical simulations.

Findings

Mass of topological quantum particle diverges for $d \,\geq\, 4$.

Finite size effects are significantly influenced by the topological excitation mass.

Theoretical predictions align with recent numerical simulation results.

Abstract

We consider the spontaneously broken regime of the $O(n)$ vector model in $d=n+1$ space-time dimensions, with boundary conditions enforcing the presence of a topological defect line. Comparing theory and finite size dependence of one-point functions observed in recent numerical simulations we argue that the mass of the underlying topological quantum particle becomes infinite when $d\geq 4$.