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arXiv · 2406.19386

Robust Hilbert space fragmentation in group-valued loop models

Alexey Khudorozhkov·Charles Stahl·Oliver Hart·Rahul Nandkishore
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Abstract

We introduce a large class of models exhibiting robust ergodicity breaking in quantum dynamics. Our work is inspired by recent discussions of "topologically robust Hilbert space fragmentation," but massively generalizes in two directions: firstly from states describable as "loop-soups" to a broader class of states reminiscent of string-nets and sponges, and secondly from models restricted to square or cubic lattices, to models defined on arbitrary lattices (and even arbitrary graphs without translation invariance). Our constructions leverage a recently proposed group-theory framework [PRX 14, 021034 (2024)], and identify a host of new phenomena arising from the interplay of "group-model dynamics" and lattice structure. We make crisp connections to gauge theories, and our construction generalizes Kitaev's quantum double to infinite groups.

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cond-mat.stat-mechcond-mat.dis-nncond-mat.str-elhep-thquant-ph

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Alexey Khudorozhkov, Charles Stahl, Oliver Hart, Rahul Nandkishore. 2024-06-27. Robust Hilbert space fragmentation in group-valued loop models. https://doi.org/10.1103/physrevb.111.024310

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