Construction and Classification of Symmetry-Protected Topological Phases in Interacting Fermion Systems

The classification and lattice model construction of symmetry-protected topological (SPT) phases in interacting fermion systems are very interesting but challenging. In this paper, we give a systematic fixed-point wave function construction of fermionic SPT (FSPT) states for generic fermionic symmet...

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Autores principales:	Qing-Rui Wang, Zheng-Cheng Gu
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2020
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/2f87bd1c5ed242019fce528f843056d1
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spelling	oai:doaj.org-article:2f87bd1c5ed242019fce528f843056d12021-12-02T11:16:59ZConstruction and Classification of Symmetry-Protected Topological Phases in Interacting Fermion Systems10.1103/PhysRevX.10.0310552160-3308https://doaj.org/article/2f87bd1c5ed242019fce528f843056d12020-09-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.10.031055http://doi.org/10.1103/PhysRevX.10.031055https://doaj.org/toc/2160-3308The classification and lattice model construction of symmetry-protected topological (SPT) phases in interacting fermion systems are very interesting but challenging. In this paper, we give a systematic fixed-point wave function construction of fermionic SPT (FSPT) states for generic fermionic symmetry group G_{f}=Z_{2}^{f}×_{ω_{2}}G_{b} which is a central extension of bosonic symmetry group G_{b} (may contain time-reversal symmetry) by the fermion parity symmetry group Z_{2}^{f}={1,P_{f}}. Our construction is based on the concept of an equivalence class of finite-depth fermionic symmetric local unitary transformations and decorating symmetry domain wall picture, subjected to certain obstructions. We also discuss the systematical construction and classification of boundary anomalous SPT states which leads to a trivialization of the corresponding bulk FSPT states. Thus, we conjecture that the obstruction-free and trivialization-free constructions naturally lead to a classification of FSPT phases. Each fixed-point wave function admits an exactly solvable commuting-projector Hamiltonian. We believe that our classification scheme can be generalized to point and space group symmetry as well as continuum Lie group symmetry.Qing-Rui WangZheng-Cheng GuAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 10, Iss 3, p 031055 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Qing-Rui Wang Zheng-Cheng Gu Construction and Classification of Symmetry-Protected Topological Phases in Interacting Fermion Systems
description	The classification and lattice model construction of symmetry-protected topological (SPT) phases in interacting fermion systems are very interesting but challenging. In this paper, we give a systematic fixed-point wave function construction of fermionic SPT (FSPT) states for generic fermionic symmetry group G_{f}=Z_{2}^{f}×_{ω_{2}}G_{b} which is a central extension of bosonic symmetry group G_{b} (may contain time-reversal symmetry) by the fermion parity symmetry group Z_{2}^{f}={1,P_{f}}. Our construction is based on the concept of an equivalence class of finite-depth fermionic symmetric local unitary transformations and decorating symmetry domain wall picture, subjected to certain obstructions. We also discuss the systematical construction and classification of boundary anomalous SPT states which leads to a trivialization of the corresponding bulk FSPT states. Thus, we conjecture that the obstruction-free and trivialization-free constructions naturally lead to a classification of FSPT phases. Each fixed-point wave function admits an exactly solvable commuting-projector Hamiltonian. We believe that our classification scheme can be generalized to point and space group symmetry as well as continuum Lie group symmetry.
format	article
author	Qing-Rui Wang Zheng-Cheng Gu
author_facet	Qing-Rui Wang Zheng-Cheng Gu
author_sort	Qing-Rui Wang
title	Construction and Classification of Symmetry-Protected Topological Phases in Interacting Fermion Systems
title_short	Construction and Classification of Symmetry-Protected Topological Phases in Interacting Fermion Systems
title_full	Construction and Classification of Symmetry-Protected Topological Phases in Interacting Fermion Systems
title_fullStr	Construction and Classification of Symmetry-Protected Topological Phases in Interacting Fermion Systems
title_full_unstemmed	Construction and Classification of Symmetry-Protected Topological Phases in Interacting Fermion Systems
title_sort	construction and classification of symmetry-protected topological phases in interacting fermion systems
publisher	American Physical Society
publishDate	2020
url	https://doaj.org/article/2f87bd1c5ed242019fce528f843056d1
work_keys_str_mv	AT qingruiwang constructionandclassificationofsymmetryprotectedtopologicalphasesininteractingfermionsystems AT zhengchenggu constructionandclassificationofsymmetryprotectedtopologicalphasesininteractingfermionsystems
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Construction and Classification of Symmetry-Protected Topological Phases in Interacting Fermion Systems

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