Disentangling Interacting Symmetry-Protected Phases of Fermions in Two Dimensions

We construct fixed point lattice models for group supercohomology symmetry-protected topological phases of fermions (2+1)D. A key feature of our approach is to construct finite depth circuits of local unitaries that explicitly build the ground states from a tensor product state. We then recover the...

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Autores principales:	Tyler D. Ellison, Lukasz Fidkowski
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2019
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/fe0dbfe7a09a4da99e466788a66b86e4
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spelling	oai:doaj.org-article:fe0dbfe7a09a4da99e466788a66b86e42021-12-02T11:42:05ZDisentangling Interacting Symmetry-Protected Phases of Fermions in Two Dimensions10.1103/PhysRevX.9.0110162160-3308https://doaj.org/article/fe0dbfe7a09a4da99e466788a66b86e42019-01-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.9.011016http://doi.org/10.1103/PhysRevX.9.011016https://doaj.org/toc/2160-3308We construct fixed point lattice models for group supercohomology symmetry-protected topological phases of fermions (2+1)D. A key feature of our approach is to construct finite depth circuits of local unitaries that explicitly build the ground states from a tensor product state. We then recover the classification of fermionic symmetry-protected topological phases, including the group structure under stacking, from the algebraic composition rules of these circuits. Furthermore, we show that the circuits are symmetric, implying that the group supercohomology phases can be many-body localized. Our strategy involves first building an auxiliary bosonic model, and then fermionizing it using the duality of Chen, Kapustin, and Radicevic. One benefit of this approach is that it clearly disentangles the role of the algebraic group supercohomology data, which are used to build the auxiliary bosonic model, from that of the spin structure, which is combinatorially encoded in the lattice and enters only in the fermionization step. In particular this allows us to study our models on 2D spatial manifolds of any topology, and to define a lattice-level procedure for ungauging fermion parity.Tyler D. EllisonLukasz FidkowskiAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 9, Iss 1, p 011016 (2019)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Tyler D. Ellison Lukasz Fidkowski Disentangling Interacting Symmetry-Protected Phases of Fermions in Two Dimensions
description	We construct fixed point lattice models for group supercohomology symmetry-protected topological phases of fermions (2+1)D. A key feature of our approach is to construct finite depth circuits of local unitaries that explicitly build the ground states from a tensor product state. We then recover the classification of fermionic symmetry-protected topological phases, including the group structure under stacking, from the algebraic composition rules of these circuits. Furthermore, we show that the circuits are symmetric, implying that the group supercohomology phases can be many-body localized. Our strategy involves first building an auxiliary bosonic model, and then fermionizing it using the duality of Chen, Kapustin, and Radicevic. One benefit of this approach is that it clearly disentangles the role of the algebraic group supercohomology data, which are used to build the auxiliary bosonic model, from that of the spin structure, which is combinatorially encoded in the lattice and enters only in the fermionization step. In particular this allows us to study our models on 2D spatial manifolds of any topology, and to define a lattice-level procedure for ungauging fermion parity.
format	article
author	Tyler D. Ellison Lukasz Fidkowski
author_facet	Tyler D. Ellison Lukasz Fidkowski
author_sort	Tyler D. Ellison
title	Disentangling Interacting Symmetry-Protected Phases of Fermions in Two Dimensions
title_short	Disentangling Interacting Symmetry-Protected Phases of Fermions in Two Dimensions
title_full	Disentangling Interacting Symmetry-Protected Phases of Fermions in Two Dimensions
title_fullStr	Disentangling Interacting Symmetry-Protected Phases of Fermions in Two Dimensions
title_full_unstemmed	Disentangling Interacting Symmetry-Protected Phases of Fermions in Two Dimensions
title_sort	disentangling interacting symmetry-protected phases of fermions in two dimensions
publisher	American Physical Society
publishDate	2019
url	https://doaj.org/article/fe0dbfe7a09a4da99e466788a66b86e4
work_keys_str_mv	AT tylerdellison disentanglinginteractingsymmetryprotectedphasesoffermionsintwodimensions AT lukaszfidkowski disentanglinginteractingsymmetryprotectedphasesoffermionsintwodimensions
_version_	1718395379768098816

Disentangling Interacting Symmetry-Protected Phases of Fermions in Two Dimensions

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