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  • Letter

Fractional vortices, Z2 gauge theory, and the confinement-deconfinement transition

Zhi-Qiang Gao1, Yen-Ta Huang1, and Dung-Hai Lee1,2,*

  • 1Department of Physics, University of California, Berkeley, California 94720, USA
  • 2Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

  • *Corresponding author: dunghai@berkeley.edu
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Phys. Rev. B 106, L121105 – Published 12 September, 2022

DOI: https://doi.org/10.1103/PhysRevB.106.L121105

Abstract

In this Letter we discuss the classical three-dimensional XY model whose nearest-neighbor interaction is a mixture of cos(θi−θj) (ferromagnetic) and cos2(θi−θj) (nematic). This model is dual to a theory with integer and half-integer vortices. While both types of vortices interact with a noncompact U(1) gauge field, the half-integer vortices interact with an extra interaction mediated by a Z2 gauge field. We shall discuss the confinement-deconfinement transition of the half-integer vortices, the Wilson and the ‘t Hooft loops, and their mutual statistics in path integral language. In addition, we shall present a quantum version of the classical model which exhibits these physics.

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Phys. Rev. B 106, L121105– Published 12 September, 2022
  • Received 23 May 2022
  • Revised 8 August 2022
  • Accepted 31 August 2022
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