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arXiv:2505.23853 · Communications Physics

Roughening and dynamics of an electric flux string in a (2+1)D lattice gauge theory

Francesco Di Marcantonio, Sunny Pradhan, Sofia Vallecorsa, Mari Carmen Bañuls, Enrique Rico Ortega

Published May 17, 2026• 3 citations
arXivHTMLPDF

Abstract

The roughening transition in Z2 lattice gauge theory remains a complex phenomenon, particularly in understanding the behavior of electric flux strings. Here, the authors use numerical simulations with matrix product states to reveal the universal Lüscher correction and distinct entanglement entropy growth, offering insights into string dynamics and symmetry restoration near deconfinement.

DOI
10.1038/s42005-026-02659-8

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The roughening transition in Z2 lattice gauge theory remains a complex phenomenon, particularly in understanding the behavior of electric flux strings. Here, the authors use numerical simulations with matrix product states to reveal the universal Lüscher correction and distinct entanglement entropy growth, offering insights into string dynamics and symmetry restoration near deconfinement.
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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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Understanding real-time string dynamics in three spatial dimensions is essential for connecting quantum simulations of lattice gauge theories (LGTs) to the physical dimensionality of QED and QCD, where transverse fluctuations and competing local processes proliferate. We present the first real-time simulations of string breaking in 3+13+13+1D lattice quantum electrodynamics. Using tree tensor networks, we simulate the quench dynamics of electric flux strings in a 3 ⁣+ ⁣13\!+\!13+1D U(1) LGT with dynamical matter. At strong coupling, the string breaks resonantly at a sharp resonance condition of mass and gauge couplings, converting electric energy into matter--antimatter pairs that screen the static charges. Off resonance, we classify all competing channels---pair production, string deformations and extensions, and flux loops---whose multiplicity, extensive for pair production and flux loops, depletes the string sector even far from resonance. A channel-resolved perturbation theory quantitatively reproduces these dynamics and their Fourier spectrum. Our results establish diagnostics and benchmarks for upcoming quantum simulators of higher-dimensional LGTs.
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