Topological insulators in odd dimensions are characterized by topological numbers. We prove the well-known relation between the topological number given by the Chern character of the Berry curvature and the Chern-Simons level of the low energy effective action for a general class of Hamiltonians bilinear in the fermion with general U(1) gauge interactions including nonminimal couplings by an explicit calculation. A series of Ward-Takahashi identities are crucial to relate the Chern-Simons level to a winding number, which could then be directly reduced to Chern character of Berry curvature by carrying out the integral over the temporal momenta.
{ "_oai": { "updated": "2021-08-29T13:32:54Z", "id": "oai:repo.scoap3.org:53772", "sets": [ "PRD" ] }, "authors": [ { "raw_name": "Hidenori Fukaya", "affiliations": [ { "country": "Japan", "value": "Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan" } ], "surname": "Fukaya", "given_names": "Hidenori", "full_name": "Fukaya, Hidenori" }, { "raw_name": "Tetsuya Onogi", "affiliations": [ { "country": "Japan", "value": "Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan" } ], "surname": "Onogi", "given_names": "Tetsuya", "full_name": "Onogi, Tetsuya" }, { "raw_name": "Satoshi Yamaguchi", "affiliations": [ { "country": "Japan", "value": "Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan" } ], "surname": "Yamaguchi", "given_names": "Satoshi", "full_name": "Yamaguchi, Satoshi" }, { "raw_name": "Xi Wu", "affiliations": [ { "country": "Israel", "value": "Physics Department, Ariel University, Ariel" } ], "surname": "Wu", "given_names": "Xi", "full_name": "Wu, Xi" } ], "titles": [ { "source": "APS", "title": "Thouless-Kohmoto-Nightingale-den Nijs formula for a general Hamiltonian" } ], "dois": [ { "value": "10.1103/PhysRevD.101.074507" } ], "publication_info": [ { "journal_volume": "101", "journal_title": "Physical Review D", "material": "article", "journal_issue": "7", "year": 2020 } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2021-08-25T10:42:47.009034", "source": "APS", "method": "APS", "submission_number": "810b323c058f11ecb53772fd3742099d" }, "page_nr": [ 12 ], "license": [ { "url": "https://creativecommons.org/licenses/by/4.0/", "license": "CC-BY-4.0" } ], "copyright": [ { "statement": "Published by the American Physical Society", "year": "2020" } ], "control_number": "53772", "record_creation_date": "2020-04-14T16:30:07.684253", "_files": [ { "checksum": "md5:eed11a5cbcb61821f6656eef6062e3ab", "filetype": "pdf", "bucket": "eb55ec49-0076-41c0-9b56-c624315ace83", "version_id": "b502175d-a8a9-41da-92e7-7f983522868e", "key": "10.1103/PhysRevD.101.074507.pdf", "size": 208814 }, { "checksum": "md5:bc56d27b4ef9bdde67082dc597166c10", "filetype": "xml", "bucket": "eb55ec49-0076-41c0-9b56-c624315ace83", "version_id": "5acd3968-290b-43ad-9b4f-fba2d904ba95", "key": "10.1103/PhysRevD.101.074507.xml", "size": 329175 } ], "collections": [ { "primary": "HEP" }, { "primary": "Citeable" }, { "primary": "Published" } ], "arxiv_eprints": [ { "categories": [ "hep-th", "cond-mat.mes-hall", "hep-lat" ], "value": "1903.11852" } ], "abstracts": [ { "source": "APS", "value": "Topological insulators in odd dimensions are characterized by topological numbers. We prove the well-known relation between the topological number given by the Chern character of the Berry curvature and the Chern-Simons level of the low energy effective action for a general class of Hamiltonians bilinear in the fermion with general U(1) gauge interactions including nonminimal couplings by an explicit calculation. A series of Ward-Takahashi identities are crucial to relate the Chern-Simons level to a winding number, which could then be directly reduced to Chern character of Berry curvature by carrying out the integral over the temporal momenta." } ], "imprints": [ { "date": "2020-04-10", "publisher": "APS" } ] }