Jiangzhi Chen, Zi Wang, Yu-Tao Tan, Ce Wang, Jie Ren
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We demonstrate that the approach successfully identifies different topological elements, such as unlink, unknot, Hopf link, Solomon ring, trefoil, and so on, by employing generalized Gell-Mann matrices in non-Hermitian models with n=2 and n=3 energy bands. Moreover, since eigenstate information of non-Hermitian bands is incorporated in addition to eigenvalues, the approach distinguishes the different parity-time symmetry and breaking phases, recognizes the opposite chirality of braids and knots, and identifies out distinct topological phases that were overlooked before. Our study shows significant potential of machine learning in classification of knots, braid groups, and non-Hermitian topological phases. The topology of braids and knots plays a central role in the understanding of many physical systems. In this paper, the authors demonstrate that unsupervised learning can be used to fully classify the braid group and knot topology associated with the bands of non-Hermitian systems, without requiring any prior information such as mathematical knowledge of topological invariants","PeriodicalId":10540,"journal":{"name":"Communications Physics","volume":null,"pages":null},"PeriodicalIF":5.4000,"publicationDate":"2024-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.nature.com/articles/s42005-024-01710-w.pdf","citationCount":"0","resultStr":"{\"title\":\"Machine learning of knot topology in non-Hermitian band braids\",\"authors\":\"Jiangzhi Chen, Zi Wang, Yu-Tao Tan, Ce Wang, Jie Ren\",\"doi\":\"10.1038/s42005-024-01710-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The deep connection among braids, knots and topological physics has provided valuable insights into studying topological states in various physical systems. However, identifying distinct braid groups and knot topology embedded in non-Hermitian systems is challenging and requires significant efforts. Here, we demonstrate that an unsupervised learning with the representation basis of su(n) Lie algebra on n-fold extended non-Hermitian bands can fully classify braid group and knot topology therein, without requiring any prior mathematical knowledge or any pre-defined topological invariants. We demonstrate that the approach successfully identifies different topological elements, such as unlink, unknot, Hopf link, Solomon ring, trefoil, and so on, by employing generalized Gell-Mann matrices in non-Hermitian models with n=2 and n=3 energy bands. Moreover, since eigenstate information of non-Hermitian bands is incorporated in addition to eigenvalues, the approach distinguishes the different parity-time symmetry and breaking phases, recognizes the opposite chirality of braids and knots, and identifies out distinct topological phases that were overlooked before. Our study shows significant potential of machine learning in classification of knots, braid groups, and non-Hermitian topological phases. The topology of braids and knots plays a central role in the understanding of many physical systems. 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Machine learning of knot topology in non-Hermitian band braids
The deep connection among braids, knots and topological physics has provided valuable insights into studying topological states in various physical systems. However, identifying distinct braid groups and knot topology embedded in non-Hermitian systems is challenging and requires significant efforts. Here, we demonstrate that an unsupervised learning with the representation basis of su(n) Lie algebra on n-fold extended non-Hermitian bands can fully classify braid group and knot topology therein, without requiring any prior mathematical knowledge or any pre-defined topological invariants. We demonstrate that the approach successfully identifies different topological elements, such as unlink, unknot, Hopf link, Solomon ring, trefoil, and so on, by employing generalized Gell-Mann matrices in non-Hermitian models with n=2 and n=3 energy bands. Moreover, since eigenstate information of non-Hermitian bands is incorporated in addition to eigenvalues, the approach distinguishes the different parity-time symmetry and breaking phases, recognizes the opposite chirality of braids and knots, and identifies out distinct topological phases that were overlooked before. Our study shows significant potential of machine learning in classification of knots, braid groups, and non-Hermitian topological phases. The topology of braids and knots plays a central role in the understanding of many physical systems. In this paper, the authors demonstrate that unsupervised learning can be used to fully classify the braid group and knot topology associated with the bands of non-Hermitian systems, without requiring any prior information such as mathematical knowledge of topological invariants
期刊介绍:
Communications Physics is an open access journal from Nature Research publishing high-quality research, reviews and commentary in all areas of the physical sciences. Research papers published by the journal represent significant advances bringing new insight to a specialized area of research in physics. We also aim to provide a community forum for issues of importance to all physicists, regardless of sub-discipline.
The scope of the journal covers all areas of experimental, applied, fundamental, and interdisciplinary physical sciences. Primary research published in Communications Physics includes novel experimental results, new techniques or computational methods that may influence the work of others in the sub-discipline. We also consider submissions from adjacent research fields where the central advance of the study is of interest to physicists, for example material sciences, physical chemistry and technologies.