Heisenberg model on a space with negative curvature: topological spin textures on the pseudosphere

TL;DR

This paper explores the behavior of Heisenberg spins on a negatively curved pseudosphere, revealing that stable solitons are impossible, but fractional solutions and non-confining vortices can exist, affecting topological spin textures.

Contribution

It demonstrates the absence of stable solitons on the pseudosphere and introduces fractional solutions stabilized by holes, along with non-confining vortex interactions.

Findings

Stable solitons cannot form on the pseudosphere.

Fractional solutions are stabilized by holes.

Vortex-antivortex pairs can dissociate at low temperatures.

Abstract

Heisenberg-like spins lying on the pseudosphere (a 2-dimensional infinite space with constant negative curvature) cannot give rise to stable soliton solutions. Only fractional solutions can be stabilized on this surface provided that at least a hole is incorporated. We also address the issue of `in-plane' vortices, in the XY regime. Interestingly, the energy of a single vortex no longer blows up as the excitation spreads to infinity. This yields a non-confining potential between a vortex and a antivortex at large distances so that the pair may dissociate at arbitrarily low temperature.