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Loop charges and fragmentation in pairwise difference conserving circuits

Pavel Orlov1,2, Cheryne Jonay1, and Tomaž Prosen1,3

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Phys. Rev. B 114, 115133 – Published 26 August, 2026

DOI: https://doi.org/10.1103/gwgn-vp7k

Abstract

In this work, we introduce a broad class of circuits, or quantum cellular automata, which we call pairwise difference conserving (PDC) circuits. These models are characterized by local gates that preserve the pairwise difference of local operators (e.g., particle number). Such circuits can be defined on arbitrary graphs in arbitrary dimensions for both quantum and classical degrees of freedom. A key consequence of PDC construction is the emergence of an extensive set of loop charges associated with closed walks of even length on the graph. These charges exhibit a one-dimensional character reminiscent of 1-form symmetries and lead to strong Hilbert space fragmentation. As a case study, we analyze a quasi-one-dimensional ladder geometry, where we characterize all dynamically disconnected sectors by the loop-charge symmetries, providing a complete decomposition of the Hilbert space. For the ladder geometry, we observe clear signatures of nonergodic dynamics even within the largest symmetry sector.

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Phys. Rev. B 114, 115133– Published 26 August, 2026
  • Received 5 June 2026
  • Accepted 12 August 2026
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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.

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