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Vortex wall phase in the fractonic XY-plaquette model on a square lattice

A. M. Begun1,2, M. N. Chernodub3,4, V. A. Goy2,5, and A. V. Molochkov6,3

  • 1Nordita, Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden
  • 2Pacific Quantum Center, Far Eastern Federal University, Vladivostok 690922, Russia
  • 3Institut Denis Poisson UMR 7013, Université de Tours, 37200 Tours, France
  • 4Department of Physics, West University of Timişoara, Boulevard Vasile Pârvan 4, Timişoara 300223, Romania
  • 5Institute of Automation and Control Processes, Far Eastern Branch, Russian Academy of Science, 5 Radio Strasse, Vladivostok 690041, Russia
  • 6Beijing Institute of Mathematical Sciences and Applications, Tsinghua University, Beijing 101408, China

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Phys. Rev. B 112, 035411 – Published 11 July, 2025

DOI: https://doi.org/10.1103/y3yg-zkzv

Abstract

The XY-plaquette model is the most straightforward lattice realization of a broad class of fractonic field theories that host quasiparticles with restricted mobility. The plaquette interaction appears naturally as a ring-exchange term in the low-energy description of exciton Bose liquids, cold atomic gases, and quantum dimer models. Using first-principle Monte Carlo simulations, we study the phase diagram and the vortex dynamics in the XY-plaquette model on a square lattice in two spatial dimensions. In its minimal formulation, the model contains a ring-exchange plaquette term in two spatial dimensions and a standard XY-link term in the (imaginary) time direction. We show that the phase diagram of the minimal XY-plaquette model possesses two phases: (i) a disordered vortex-dominated phase in which a single percolating vortex trajectory occupies the whole three-dimensional spacetime; (ii) a partially disordered phase in which the vortices become partially immobile, with their worldlines strictly confined to one or several infinite two-dimensional planes. The spatial positions and spatial orientations (along x or y axis) of these vortex domain walls appear to be spontaneous. Individual vortices form a disordered system within each vortex domain wall, so the fractal spacetime dimension of vortex trajectories approaches Df=2. We argue that the appearance of the vortex walls could be interpreted as a consequence of the spontaneous breaking of a global internal symmetry in the compact XY-plaquette model.

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Phys. Rev. B 112, 035411– Published 11 July, 2025
  • Received 8 October 2024
  • Revised 15 May 2025
  • Accepted 10 June 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by Bibsam.

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