Loop Charges and Fragmentation in Pairwise Difference Conserving Circuits
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914107563704320 |
|---|---|
| author | Orlov, Pavel Jonay, Cheryne Prosen, Tomaž |
| author_facet | Orlov, Pavel Jonay, Cheryne Prosen, Tomaž |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_18992 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Loop Charges and Fragmentation in Pairwise Difference Conserving Circuits Orlov, Pavel Jonay, Cheryne Prosen, Tomaž Statistical Mechanics 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. |
| title | Loop Charges and Fragmentation in Pairwise Difference Conserving Circuits |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2510.18992 |