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Tensor-Network Study of the Roughening Transition in a (2+1)D Z2 Lattice Gauge Theory with Matter

Wen-Tao Xu, Michael Knap, and Frank Pollmann

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Phys. Rev. Lett. 135, 036503 – Published 17 July, 2025

DOI: https://doi.org/10.1103/3lxj-dx76

Abstract

Within the confined phase of (2+1)D lattice gauge theories a roughening transition arises between a weakly confined regime with floppy string excitations and a strongly confined regime with stiff string excitations. In this Letter, we use an infinite Density Matrix Renormalization Group (iDMRG) algorithm to quantitatively characterize the properties of confined strings. To this end, we stabilize the state with a string excitation by ’t Hooft loop operators. While for zero gauge-matter coupling we can use bare ’t Hooft loop operators to do so, for finite gauge-matter coupling we have to transform them to emergent ones, which we achieve with an adiabatic protocol. By analyzing the scaling of both a novel order parameter and the entanglement entropy, our approach allows us to accurately determine the roughening transition, even at finite gauge-matter coupling.

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Phys. Rev. Lett. 135, 036503– Published 17 July, 2025
  • Received 26 March 2025
  • Revised 3 May 2025
  • Accepted 27 June 2025
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