Quantum Interactions of Topological Solitons from Electrodynamics

TL;DR

This paper investigates the quantum interactions of topological solitons in 2D quantum antiferromagnets, revealing a short-range attraction and a universal long-range repulsion through a novel path-integral approach.

Contribution

It introduces a flexible framework using worldline formulation to analyze quantum fluctuations and interactions of solitons, surpassing traditional scattering methods.

Findings

Identified a short-range attractive potential between solitons.

Discovered a universal long-range repulsive $1/r$ potential.

Developed a new method for calculating quantum interactions in soliton systems.

Abstract

The Casimir energy for the classically stable configurations of the topological solitons in 2D quantum antiferromagnets is studied by performing the path-integral over quantum fluctuations. The magnon fluctuation around the solitons saturating the Bogomol'nyi inequality may be viewed as a charged scalar field coupled with an effective magnetic field induced by the solitons. The magnon-soliton couping is closely related to the Pauli Hamiltonian, with which the effective action is calculated by adapting the worldline formulation of the derivative expansion for the 2+1d quantum electrodynamics in an external field. The resulting framework is more flexible than the conventional scattering analysis based on the Dashen-Hasslacher-Neveu formula. We obtain a short-range attractive well and a universal long-range $1/r$-type repulsive potential between two solitons.