{"title":"准自由费米子的\\({\\mathbb {Z}}_{2}\\) -拓扑指数","authors":"N. J. B. Aza, A. F. Reyes-Lega, L. A. M. Sequera","doi":"10.1007/s11040-022-09421-w","DOIUrl":null,"url":null,"abstract":"<div><p>We use infinite dimensional self-dual <span>\\(\\mathrm {CAR}\\)</span> <span>\\(C^{*}\\)</span>-algebras to study a <span>\\({\\mathbb {Z}}_{2}\\)</span>-index, which classifies free-fermion systems embedded on <span>\\({\\mathbb {Z}}^{d}\\)</span> disordered lattices. Combes–Thomas estimates are pivotal to show that the <span>\\({\\mathbb {Z}}_{2}\\)</span>-index is uniform with respect to the size of the system. We additionally deal with the set of ground states to completely describe the mathematical structure of the underlying system. Furthermore, the weak<span>\\(^{*}\\)</span>-topology of the set of linear functionals is used to analyze paths connecting different sets of ground states.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"25 2","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2022-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A \\\\({\\\\mathbb {Z}}_{2}\\\\)-Topological Index for Quasi-Free Fermions\",\"authors\":\"N. J. B. Aza, A. F. Reyes-Lega, L. A. M. Sequera\",\"doi\":\"10.1007/s11040-022-09421-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We use infinite dimensional self-dual <span>\\\\(\\\\mathrm {CAR}\\\\)</span> <span>\\\\(C^{*}\\\\)</span>-algebras to study a <span>\\\\({\\\\mathbb {Z}}_{2}\\\\)</span>-index, which classifies free-fermion systems embedded on <span>\\\\({\\\\mathbb {Z}}^{d}\\\\)</span> disordered lattices. Combes–Thomas estimates are pivotal to show that the <span>\\\\({\\\\mathbb {Z}}_{2}\\\\)</span>-index is uniform with respect to the size of the system. We additionally deal with the set of ground states to completely describe the mathematical structure of the underlying system. Furthermore, the weak<span>\\\\(^{*}\\\\)</span>-topology of the set of linear functionals is used to analyze paths connecting different sets of ground states.</p></div>\",\"PeriodicalId\":694,\"journal\":{\"name\":\"Mathematical Physics, Analysis and Geometry\",\"volume\":\"25 2\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2022-03-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Physics, Analysis and Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11040-022-09421-w\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Physics, Analysis and Geometry","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s11040-022-09421-w","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
A \({\mathbb {Z}}_{2}\)-Topological Index for Quasi-Free Fermions
We use infinite dimensional self-dual \(\mathrm {CAR}\)\(C^{*}\)-algebras to study a \({\mathbb {Z}}_{2}\)-index, which classifies free-fermion systems embedded on \({\mathbb {Z}}^{d}\) disordered lattices. Combes–Thomas estimates are pivotal to show that the \({\mathbb {Z}}_{2}\)-index is uniform with respect to the size of the system. We additionally deal with the set of ground states to completely describe the mathematical structure of the underlying system. Furthermore, the weak\(^{*}\)-topology of the set of linear functionals is used to analyze paths connecting different sets of ground states.
期刊介绍:
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