Fluctuations and vortex pattern ordering in fully frustrated XY model with honeycomb lattice

TL;DR

This study investigates the ground state degeneracy and vortex pattern ordering in a fully frustrated XY model on a honeycomb lattice, revealing hidden symmetries and the conditions needed for vortex order observation.

Contribution

It demonstrates that ground state degeneracy persists despite harmonic fluctuations due to hidden gauge symmetry, and identifies the role of anharmonic fluctuations in vortex pattern selection.

Findings

Degeneracy survives harmonic fluctuations due to hidden gauge symmetry.

Vortex ordering appears only with anharmonic fluctuations.

Large system sizes are necessary to observe vortex ordering.

Abstract

The accidental degeneracy of various ground states in a fully frustrated XY model with a honeycomb lattice is shown to survive even when the free energy of the harmonic fluctuations is taken into account. The reason for that consists in the existence of a hidden gauge symmetry between the Hamiltonians describing the harmonic fluctuations in all these ground states. A particular vortex pattern is selected only when anharmonic fluctuations are taken into account. However, the observation of vortex ordering requires relatively large system size L>>100000.