Topology and metastability in the lattice Skyrme model

TL;DR

This paper develops a fully quantized lattice Skyrme model as an effective field theory for baryon-meson interactions, revealing that skyrmions shrink with increased fluctuations due to metastable states at finite temperature.

Contribution

It introduces a lattice Skyrme model with a novel topological density and calculates skyrmion size, showing unexpected shrinking behavior under thermal and quantum fluctuations.

Findings

Skyrmion size decreases with temperature and quantum fluctuations.

Large number of metastable states become accessible at higher temperatures.

Provides a new method to compute topological properties on a lattice.

Abstract

We offer the Skyrme model on a lattice as an effective field theory - fully quantized - of baryon-meson interactions at temperatures below the chiral phase transition. We define a local topological density that involves the volumes of tetrahedra in the target space S^3 and we make use of Coxeter's formula for the Schlafli function to implement it. This permits us to calculate the mean-square radius of a skyrmion in the three-dimensional lattice Skyrme model, which may be viewed as a Ginzburg-Landau effective theory for the full quantum theory at finite temperature. We find that, contrary to expectations, the skyrmion shrinks as quantum and thermal fluctuations are enhanced. We ascribe this to a large number of metastable states that become accessible as the temperature is raised.