Dual View of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">Z</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math>-Gauged XY Model in 3D

Piers Coleman; Anatoly Kuklov; Alexei Tsvelik

doi:10.1103/nf4j-kbtj

Dual View of the $Z_{2}$ -Gauged XY Model in 3D

Piers Coleman ^1,2, Anatoly Kuklov ³, and Alexei Tsvelik⁴

¹Center for Materials Theory, Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Rd., Piscataway, NJ 08854-8019, USA
²Department of Physics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK
³Department of Physics and Astronomy, CSI, and the Graduate Center of CUNY, New York, USA
⁴Division of Condensed Matter Physics and Materials Science, Brookhaven National Laboratory, Upton, New York 11973-5000, USA

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Phys. Rev. Lett. 134, 236001 – Published 9 June, 2025

DOI: https://doi.org/10.1103/nf4j-kbtj

Abstract

The $Z_{2}$ -gauged XY model is of long-standing interest both in the context of nematic order, and the study of fractionalization and superconductivity. This Letter presents heuristic arguments that no deconfinement of the XY field occurs in this model and presents results of a large-scale Monte Carlo simulations on a cubic lattice that are consistent with this conclusion. The correlation radius determining the confinement is found to be growing rapidly as a function of the parameters in the phase featuring the nematic order. Thus, mesoscopic properties of the system can mimic deconfinement with high accuracy in some part of the phase diagram.

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Dual View of the Z2-Gauged XY Model in 3D

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Dual View of the $Z_{2}$ -Gauged XY Model in 3D