二维环形编码中的低纠缠激励融合

arXiv - PHYS - Strongly Correlated Electrons Pub Date : 2024-09-11 DOI:arxiv-2409.07544

Jing-Yu Zhao, Xie Chen

{"title":"二维环形编码中的低纠缠激励融合","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":"{\"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}","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}