Duality and stacking of bosonic and fermionic SPT phases
Abstract We study the interplay of duality and stacking of bosonic and fermionic symmetry-protected topological phases in one spatial dimension. In general the classifications of bosonic and fermionic phases have different group structures under the operation of stacking, but we argue that they are...
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2024-10-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP10(2024)034 |
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| author | Alex Turzillo Minyoung You |
| author_facet | Alex Turzillo Minyoung You |
| author_sort | Alex Turzillo |
| collection | DOAJ |
| description | Abstract We study the interplay of duality and stacking of bosonic and fermionic symmetry-protected topological phases in one spatial dimension. In general the classifications of bosonic and fermionic phases have different group structures under the operation of stacking, but we argue that they are often isomorphic and give an explicit isomorphism when it exists. This occurs for all unitary symmetry groups and many groups with antiunitary symmetries, which we characterize. We find that this isomorphism is typically not implemented by the Jordan-Wigner transformation, nor is it a consequence of any other duality transformation that falls within the framework of topological holography. Along the way to this conclusion, we recover the fermionic stacking rule in terms of G $$ \mathcal{G} $$ -pin partition functions, give a gauge-invariant characterization of the twisted group cohomology invariant, and state a procedure for stacking gapped phases in the formalism of symmetry topological field theory. |
| format | Article |
| id | doaj-art-631f398750ed4d24b0167c8f42f9c81e |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-631f398750ed4d24b0167c8f42f9c81e2024-12-08T12:11:09ZengSpringerOpenJournal of High Energy Physics1029-84792024-10-0120241014710.1007/JHEP10(2024)034Duality and stacking of bosonic and fermionic SPT phasesAlex Turzillo0Minyoung You1Perimeter Institute for Theoretical PhysicsPOSTECH Basic Science Research InstituteAbstract We study the interplay of duality and stacking of bosonic and fermionic symmetry-protected topological phases in one spatial dimension. In general the classifications of bosonic and fermionic phases have different group structures under the operation of stacking, but we argue that they are often isomorphic and give an explicit isomorphism when it exists. This occurs for all unitary symmetry groups and many groups with antiunitary symmetries, which we characterize. We find that this isomorphism is typically not implemented by the Jordan-Wigner transformation, nor is it a consequence of any other duality transformation that falls within the framework of topological holography. Along the way to this conclusion, we recover the fermionic stacking rule in terms of G $$ \mathcal{G} $$ -pin partition functions, give a gauge-invariant characterization of the twisted group cohomology invariant, and state a procedure for stacking gapped phases in the formalism of symmetry topological field theory.https://doi.org/10.1007/JHEP10(2024)034Anomalies in Field and String TheoriesDiscrete SymmetriesTopological Field TheoriesTopological States of Matter |
| spellingShingle | Alex Turzillo Minyoung You Duality and stacking of bosonic and fermionic SPT phases Journal of High Energy Physics Anomalies in Field and String Theories Discrete Symmetries Topological Field Theories Topological States of Matter |
| title | Duality and stacking of bosonic and fermionic SPT phases |
| title_full | Duality and stacking of bosonic and fermionic SPT phases |
| title_fullStr | Duality and stacking of bosonic and fermionic SPT phases |
| title_full_unstemmed | Duality and stacking of bosonic and fermionic SPT phases |
| title_short | Duality and stacking of bosonic and fermionic SPT phases |
| title_sort | duality and stacking of bosonic and fermionic spt phases |
| topic | Anomalies in Field and String Theories Discrete Symmetries Topological Field Theories Topological States of Matter |
| url | https://doi.org/10.1007/JHEP10(2024)034 |
| work_keys_str_mv | AT alexturzillo dualityandstackingofbosonicandfermionicsptphases AT minyoungyou dualityandstackingofbosonicandfermionicsptphases |