We have made a detailed study of the phase structure for the lattice Schwinger model with one flavor of Wilson fermion on the plane. For numerical investigation, we develop a decorated tensor renormalization method for lattice gauge theories with fermions incorporating the Grassmann tensor renormalization. Our algorithm manifestly preserves rotation and reflection symmetries. We find not only a parity-broken phase but also a Berezinskii-Kosterlitz-Thouless (BKT) transition by evaluating the central charge and an expectation value of a projection operator into the parity-odd subspace. The BKT phase boundaries converge into the degenerated doubler pole , while the parity-breaking transition line ends at the physical pole . In addition, our analysis of scaling dimensions indicates that a conformal field theory with SU(2) symmetry arises on the line of .
{ "_oai": { "updated": "2022-03-04T10:25:47Z", "id": "oai:repo.scoap3.org:23569", "sets": [ "PRD" ] }, "authors": [ { "raw_name": "Yuya Shimizu", "affiliations": [ { "country": "Japan", "value": "RIKEN Advanced Institute for Computational Science, Kobe, Hyogo 650-0047, Japan" } ], "surname": "Shimizu", "given_names": "Yuya", "full_name": "Shimizu, Yuya" }, { "raw_name": "Yoshinobu Kuramashi", "affiliations": [ { "country": "Japan", "value": "Center for Computational Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8577, Japan" }, { "country": "Japan", "value": "RIKEN Advanced Institute for Computational Science, Kobe, Hyogo 650-0047, Japan" } ], "surname": "Kuramashi", "given_names": "Yoshinobu", "full_name": "Kuramashi, Yoshinobu" } ], "titles": [ { "source": "APS", "title": "Berezinskii-Kosterlitz-Thouless transition in lattice Schwinger model with one flavor of Wilson fermion" } ], "dois": [ { "value": "10.1103/PhysRevD.97.034502" } ], "publication_info": [ { "journal_volume": "97", "journal_title": "Physical Review D", "material": "article", "journal_issue": "3", "year": 2018 } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2020-06-29T15:41:09.422457", "source": "APS", "method": "APS", "submission_number": "b8bb8f3cb9e211eaad8602163e01809a" }, "page_nr": [ 14 ], "license": [ { "url": "https://creativecommons.org/licenses/by/4.0/", "license": "CC-BY-4.0" } ], "copyright": [ { "statement": "Published by the American Physical Society", "year": "2018" } ], "control_number": "23569", "record_creation_date": "2018-06-08T06:05:52.469483", "_files": [ { "checksum": "md5:54772f1b704f992d467970fa7e9b2d47", "filetype": "pdf", "bucket": "9d4acecd-96cc-4d93-8069-c856714fe96e", "version_id": "00875bdc-3506-4d06-8256-e55362b37937", "key": "10.1103/PhysRevD.97.034502.pdf", "size": 1216511 }, { "checksum": "md5:d50a8ef0c76865bf14c207013c33d90c", "filetype": "xml", "bucket": "9d4acecd-96cc-4d93-8069-c856714fe96e", "version_id": "6288772e-bfa2-43a3-96de-90280e763785", "key": "10.1103/PhysRevD.97.034502.xml", "size": 406870 } ], "collections": [ { "primary": "HEP" }, { "primary": "Citeable" }, { "primary": "Published" } ], "arxiv_eprints": [ { "categories": [ "hep-lat", "cond-mat.str-el", "quant-ph" ], "value": "1712.07808" } ], "abstracts": [ { "source": "APS", "value": "We have made a detailed study of the phase structure for the lattice Schwinger model with one flavor of Wilson fermion on the <math><mrow><mo>(</mo><mi>m</mi><mo>,</mo><mi>g</mi><mo>)</mo></mrow></math> plane. For numerical investigation, we develop a decorated tensor renormalization method for lattice gauge theories with fermions incorporating the Grassmann tensor renormalization. Our algorithm manifestly preserves rotation and reflection symmetries. We find not only a parity-broken phase but also a Berezinskii-Kosterlitz-Thouless (BKT) transition by evaluating the central charge and an expectation value of a projection operator into the parity-odd subspace. The BKT phase boundaries converge into the degenerated doubler pole <math><mo>(</mo><mi>m</mi><mo>,</mo><mi>g</mi><mo>)</mo><mo>=</mo><mo>(</mo><mo>\u2212</mo><mn>2</mn><mo>,</mo><mn>0</mn><mo>)</mo></math>, while the parity-breaking transition line ends at the physical pole <math><mo>(</mo><mi>m</mi><mo>,</mo><mi>g</mi><mo>)</mo><mo>=</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></math>. In addition, our analysis of scaling dimensions indicates that a conformal field theory with SU(2) symmetry arises on the line of <math><mi>m</mi><mo>=</mo><mo>\u2212</mo><mn>2</mn></math>." } ], "imprints": [ { "date": "2018-02-06", "publisher": "APS" } ] }