{"title":"Fusion of Low-Entanglement Excitations in 2D Toric Code","authors":"Jing-Yu Zhao, Xie Chen","doi":"arxiv-2409.07544","DOIUrl":null,"url":null,"abstract":"On top of a $D$-dimensional gapped bulk state, Low Entanglement Excitations\n(LEE) on $d$($<D$)-dimensional sub-manifolds can have extensive energy but\npreserves the entanglement area law of the ground state. Due to their\nmulti-dimensional nature, the LEEs embody a higher-category structure in\nquantum systems. They are the ground state of a modified Hamiltonian and hence\ncapture the notions of `defects' of generalized symmetries. In previous works,\nwe studied the low-entanglement excitations in a trivial phase as well as those\nin invertible phases. We find that LEEs in these phases have the same structure\nas lower-dimensional gapped phases and their defects within. In this paper, we\nstudy the LEEs inside non-invertible topological phases. We focus on the simple\nexample of $\\mathbb{Z}_2$ toric code and discuss how the fusion result of 1d\nLEEs with 0d morphisms can depend on both the choice of fusion circuit and the\nordering of the fused defects.","PeriodicalId":501171,"journal":{"name":"arXiv - PHYS - Strongly Correlated Electrons","volume":"17 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Strongly Correlated Electrons","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.07544","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
On top of a $D$-dimensional gapped bulk state, Low Entanglement Excitations
(LEE) on $d$($
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