Non-Abelian topological spin liquids from arrays of quantum wires or spin chains
We construct two-dimensional non-Abelian topologically ordered states by strongly coupling arrays of one-dimensional quantum wires via interactions. In our scheme, all charge degrees of freedom are gapped, so the construction can use either quantum wires or quantum spin chains as building blocks, wi...
Gespeichert in:
| Veröffentlicht in: | Physical review. B 2016-05, Vol.93 (20), Article 205123 |
|---|---|
| Hauptverfasser: | , , , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | 20 |
| container_start_page | |
| container_title | Physical review. B |
| container_volume | 93 |
| creator | Huang, Po-Hao Chen, Jyong-Hao Gomes, Pedro R. S. Neupert, Titus Chamon, Claudio Mudry, Christopher |
| description | We construct two-dimensional non-Abelian topologically ordered states by strongly coupling arrays of one-dimensional quantum wires via interactions. In our scheme, all charge degrees of freedom are gapped, so the construction can use either quantum wires or quantum spin chains as building blocks, with the same end result. The construction gaps the degrees of freedom in the bulk, while leaving decoupled states at the edges that are described by conformal field theories (CFT) in (1+1)-dimensional space and time. We consider both the cases where time-reversal symmetry (TRS) is present or absent. When TRS is absent, the edge states are chiral and stable. We prescribe, in particular, how to arrive at all the edge states described by the unitary CFT minimal models with central charges c |
| doi_str_mv | 10.1103/PhysRevB.93.205123 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_osti_</sourceid><recordid>TN_cdi_osti_scitechconnect_1253067</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1825465850</sourcerecordid><originalsourceid>FETCH-LOGICAL-c417t-4913351fc74ee8ba4390ef2752f13b209ad00568585018d9b0440b100d280cb43</originalsourceid><addsrcrecordid>eNo9kF1LwzAUhoMoOOb-gFfBK286T77a5nIOv2DoEL0OaZq6SJtsSavs37tR9eq8HB7eFx6ELgnMCQF2s97s06v9up1LNqcgCGUnaEJ5LjMpc3n6nwWco1lKnwBAcpAFyAlaPwefLSrbOu1xH7ahDR_O6BanrfO4dbvB1Qk3MXRYx6j3CYcG7wbt-6HD3y7awyOOsNlo59MFOmt0m-zs907R-_3d2_IxW708PC0Xq8xwUvQZl4QxQRpTcGvLSnMmwTa0ELQhrKIgdQ0g8lKUAkhZywo4h4oA1LQEU3E2RVdjb0i9U8m43pqNCd5b0ytCBYO8OEDXI7SNYTfY1KvOJWPbVnsbhqRISQXPjxsHlI6oiSGlaBu1ja7Tca8IqKNm9adZSaZGzewHhMhwqA</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1825465850</pqid></control><display><type>article</type><title>Non-Abelian topological spin liquids from arrays of quantum wires or spin chains</title><source>American Physical Society Journals</source><creator>Huang, Po-Hao ; Chen, Jyong-Hao ; Gomes, Pedro R. S. ; Neupert, Titus ; Chamon, Claudio ; Mudry, Christopher</creator><creatorcontrib>Huang, Po-Hao ; Chen, Jyong-Hao ; Gomes, Pedro R. S. ; Neupert, Titus ; Chamon, Claudio ; Mudry, Christopher</creatorcontrib><description>We construct two-dimensional non-Abelian topologically ordered states by strongly coupling arrays of one-dimensional quantum wires via interactions. In our scheme, all charge degrees of freedom are gapped, so the construction can use either quantum wires or quantum spin chains as building blocks, with the same end result. The construction gaps the degrees of freedom in the bulk, while leaving decoupled states at the edges that are described by conformal field theories (CFT) in (1+1)-dimensional space and time. We consider both the cases where time-reversal symmetry (TRS) is present or absent. When TRS is absent, the edge states are chiral and stable. We prescribe, in particular, how to arrive at all the edge states described by the unitary CFT minimal models with central charges c<1. These non-Abelian spin liquid states have vanishing quantum Hall conductivities, but nonzero thermal ones. When TRS is present, we describe scenarios where the bulk state can be a non-Abelian, nonchiral, and gapped quantum spin liquid, or a gapless one. In the former case, we find that the edge states are also gapped. The paper provides a brief review of non-Abelian bosonization and affine current algebras, with the purpose of being self-contained. To illustrate the methods in a warm-up exercise, we recover the tenfold way classification of two-dimensional noninteracting topological insulators using the Majorana representation that naturally arises within non-Abelian bosonization. Within this scheme, the classification reduces to counting the number of null singular values of a mass matrix, with gapless edge modes present when left and right null eigenvectors exist.</description><identifier>ISSN: 2469-9950</identifier><identifier>EISSN: 2469-9969</identifier><identifier>DOI: 10.1103/PhysRevB.93.205123</identifier><language>eng</language><publisher>United States: American Physical Society</publisher><subject>Arrays ; Classification ; Construction ; Degrees of freedom ; Mathematical analysis ; Mathematical models ; Quantum wires ; Spin liquid</subject><ispartof>Physical review. B, 2016-05, Vol.93 (20), Article 205123</ispartof><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c417t-4913351fc74ee8ba4390ef2752f13b209ad00568585018d9b0440b100d280cb43</citedby><cites>FETCH-LOGICAL-c417t-4913351fc74ee8ba4390ef2752f13b209ad00568585018d9b0440b100d280cb43</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,776,780,881,2863,2864,27901,27902</link.rule.ids><backlink>$$Uhttps://www.osti.gov/biblio/1253067$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Huang, Po-Hao</creatorcontrib><creatorcontrib>Chen, Jyong-Hao</creatorcontrib><creatorcontrib>Gomes, Pedro R. S.</creatorcontrib><creatorcontrib>Neupert, Titus</creatorcontrib><creatorcontrib>Chamon, Claudio</creatorcontrib><creatorcontrib>Mudry, Christopher</creatorcontrib><title>Non-Abelian topological spin liquids from arrays of quantum wires or spin chains</title><title>Physical review. B</title><description>We construct two-dimensional non-Abelian topologically ordered states by strongly coupling arrays of one-dimensional quantum wires via interactions. In our scheme, all charge degrees of freedom are gapped, so the construction can use either quantum wires or quantum spin chains as building blocks, with the same end result. The construction gaps the degrees of freedom in the bulk, while leaving decoupled states at the edges that are described by conformal field theories (CFT) in (1+1)-dimensional space and time. We consider both the cases where time-reversal symmetry (TRS) is present or absent. When TRS is absent, the edge states are chiral and stable. We prescribe, in particular, how to arrive at all the edge states described by the unitary CFT minimal models with central charges c<1. These non-Abelian spin liquid states have vanishing quantum Hall conductivities, but nonzero thermal ones. When TRS is present, we describe scenarios where the bulk state can be a non-Abelian, nonchiral, and gapped quantum spin liquid, or a gapless one. In the former case, we find that the edge states are also gapped. The paper provides a brief review of non-Abelian bosonization and affine current algebras, with the purpose of being self-contained. To illustrate the methods in a warm-up exercise, we recover the tenfold way classification of two-dimensional noninteracting topological insulators using the Majorana representation that naturally arises within non-Abelian bosonization. Within this scheme, the classification reduces to counting the number of null singular values of a mass matrix, with gapless edge modes present when left and right null eigenvectors exist.</description><subject>Arrays</subject><subject>Classification</subject><subject>Construction</subject><subject>Degrees of freedom</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Quantum wires</subject><subject>Spin liquid</subject><issn>2469-9950</issn><issn>2469-9969</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNo9kF1LwzAUhoMoOOb-gFfBK286T77a5nIOv2DoEL0OaZq6SJtsSavs37tR9eq8HB7eFx6ELgnMCQF2s97s06v9up1LNqcgCGUnaEJ5LjMpc3n6nwWco1lKnwBAcpAFyAlaPwefLSrbOu1xH7ahDR_O6BanrfO4dbvB1Qk3MXRYx6j3CYcG7wbt-6HD3y7awyOOsNlo59MFOmt0m-zs907R-_3d2_IxW708PC0Xq8xwUvQZl4QxQRpTcGvLSnMmwTa0ELQhrKIgdQ0g8lKUAkhZywo4h4oA1LQEU3E2RVdjb0i9U8m43pqNCd5b0ytCBYO8OEDXI7SNYTfY1KvOJWPbVnsbhqRISQXPjxsHlI6oiSGlaBu1ja7Tca8IqKNm9adZSaZGzewHhMhwqA</recordid><startdate>20160513</startdate><enddate>20160513</enddate><creator>Huang, Po-Hao</creator><creator>Chen, Jyong-Hao</creator><creator>Gomes, Pedro R. S.</creator><creator>Neupert, Titus</creator><creator>Chamon, Claudio</creator><creator>Mudry, Christopher</creator><general>American Physical Society</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SR</scope><scope>7U5</scope><scope>8BQ</scope><scope>8FD</scope><scope>H8D</scope><scope>JG9</scope><scope>L7M</scope><scope>OTOTI</scope></search><sort><creationdate>20160513</creationdate><title>Non-Abelian topological spin liquids from arrays of quantum wires or spin chains</title><author>Huang, Po-Hao ; Chen, Jyong-Hao ; Gomes, Pedro R. S. ; Neupert, Titus ; Chamon, Claudio ; Mudry, Christopher</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c417t-4913351fc74ee8ba4390ef2752f13b209ad00568585018d9b0440b100d280cb43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Arrays</topic><topic>Classification</topic><topic>Construction</topic><topic>Degrees of freedom</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Quantum wires</topic><topic>Spin liquid</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Huang, Po-Hao</creatorcontrib><creatorcontrib>Chen, Jyong-Hao</creatorcontrib><creatorcontrib>Gomes, Pedro R. S.</creatorcontrib><creatorcontrib>Neupert, Titus</creatorcontrib><creatorcontrib>Chamon, Claudio</creatorcontrib><creatorcontrib>Mudry, Christopher</creatorcontrib><collection>CrossRef</collection><collection>Engineered Materials Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Materials Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>OSTI.GOV</collection><jtitle>Physical review. B</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Huang, Po-Hao</au><au>Chen, Jyong-Hao</au><au>Gomes, Pedro R. S.</au><au>Neupert, Titus</au><au>Chamon, Claudio</au><au>Mudry, Christopher</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Non-Abelian topological spin liquids from arrays of quantum wires or spin chains</atitle><jtitle>Physical review. B</jtitle><date>2016-05-13</date><risdate>2016</risdate><volume>93</volume><issue>20</issue><artnum>205123</artnum><issn>2469-9950</issn><eissn>2469-9969</eissn><abstract>We construct two-dimensional non-Abelian topologically ordered states by strongly coupling arrays of one-dimensional quantum wires via interactions. In our scheme, all charge degrees of freedom are gapped, so the construction can use either quantum wires or quantum spin chains as building blocks, with the same end result. The construction gaps the degrees of freedom in the bulk, while leaving decoupled states at the edges that are described by conformal field theories (CFT) in (1+1)-dimensional space and time. We consider both the cases where time-reversal symmetry (TRS) is present or absent. When TRS is absent, the edge states are chiral and stable. We prescribe, in particular, how to arrive at all the edge states described by the unitary CFT minimal models with central charges c<1. These non-Abelian spin liquid states have vanishing quantum Hall conductivities, but nonzero thermal ones. When TRS is present, we describe scenarios where the bulk state can be a non-Abelian, nonchiral, and gapped quantum spin liquid, or a gapless one. In the former case, we find that the edge states are also gapped. The paper provides a brief review of non-Abelian bosonization and affine current algebras, with the purpose of being self-contained. To illustrate the methods in a warm-up exercise, we recover the tenfold way classification of two-dimensional noninteracting topological insulators using the Majorana representation that naturally arises within non-Abelian bosonization. Within this scheme, the classification reduces to counting the number of null singular values of a mass matrix, with gapless edge modes present when left and right null eigenvectors exist.</abstract><cop>United States</cop><pub>American Physical Society</pub><doi>10.1103/PhysRevB.93.205123</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 2469-9950 |
| ispartof | Physical review. B, 2016-05, Vol.93 (20), Article 205123 |
| issn | 2469-9950 2469-9969 |
| language | eng |
| recordid | cdi_osti_scitechconnect_1253067 |
| source | American Physical Society Journals |
| subjects | Arrays Classification Construction Degrees of freedom Mathematical analysis Mathematical models Quantum wires Spin liquid |
| title | Non-Abelian topological spin liquids from arrays of quantum wires or spin chains |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-15T11%3A52%3A56IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_osti_&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Non-Abelian%20topological%20spin%20liquids%20from%20arrays%20of%20quantum%20wires%20or%20spin%20chains&rft.jtitle=Physical%20review.%20B&rft.au=Huang,%20Po-Hao&rft.date=2016-05-13&rft.volume=93&rft.issue=20&rft.artnum=205123&rft.issn=2469-9950&rft.eissn=2469-9969&rft_id=info:doi/10.1103/PhysRevB.93.205123&rft_dat=%3Cproquest_osti_%3E1825465850%3C/proquest_osti_%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1825465850&rft_id=info:pmid/&rfr_iscdi=true |