Vortex, skyrmion and elliptical domain wall textures in the two-dimensional Hubbard model

TL;DR

This paper investigates complex spin and charge textures such as vortices, skyrmions, and elliptical domain walls in the two-dimensional Hubbard model, revealing their stability and energy hierarchy through numerical analysis.

Contribution

It introduces a detailed analysis of spin textures around doped holes, identifying vortex-antivortex pairs as the most stable configuration and exploring the stability of elliptical domain walls.

Findings

Vortex-antivortex pairs are energetically favored over bipolaron configurations.

Skyrmions are local energy minima but less stable than vortices.

Elliptical domain walls are stable only at low doping and when partially filled.

Abstract

The spin and charge texture around doped holes in the two-dimensional Hubbard model is calculated within an unrestricted spin rotational invariant slave-boson approach. In the first part we examine in detail the spin structure around two holes doped in the half-filled system where we have studied cluster sizes up to 10 x 10. It turns out that the most stable configuration corresponds to a vortex-antivortex pair which has lower energy than the Neel-type bipolaron even when one takes the far field contribution into account. We also obtain skyrmions as local minima of the energy functional but with higher total energy than the vortex solutions. Additionally we have investigated the stability of elliptical domain walls for commensurate hole concentrations. We find that (i) these phases correspond to local minima of the energy functional only in case of partially filled walls, (ii) elliptical domain walls are only stable in the low doping regime.