Loop Charges and Fragmentation in Pairwise Difference Conserving Circuits
arXiv:2510.18992 · doi: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 circuits' (PDC). These models are characterized by local gates that preserve the pairwise difference of local operators (e.g. particle number). Such circuits can be de- fined on arbitrary graphs in arbitrary dimensions for both quantum and classical degrees of freedom. A key consequence of the 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 dynam- ically 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.
10 pages, 10 figures
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