Fracton Models on General Three-Dimensional Manifolds

Fracton models, a collection of exotic gapped lattice Hamiltonians recently discovered in three spatial dimensions, contain some “topological” features: They support fractional bulk excitations (dubbed fractons) and a ground-state degeneracy that is robust to local perturbations. However, because pr...

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Autores principales:	Wilbur Shirley, Kevin Slagle, Zhenghan Wang, Xie Chen
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2018
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/bff7eb400ebd4dd1bf6f77beadbfdc23
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id	oai:doaj.org-article:bff7eb400ebd4dd1bf6f77beadbfdc23
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spelling	oai:doaj.org-article:bff7eb400ebd4dd1bf6f77beadbfdc232021-12-02T11:43:13ZFracton Models on General Three-Dimensional Manifolds10.1103/PhysRevX.8.0310512160-3308https://doaj.org/article/bff7eb400ebd4dd1bf6f77beadbfdc232018-08-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.8.031051http://doi.org/10.1103/PhysRevX.8.031051https://doaj.org/toc/2160-3308Fracton models, a collection of exotic gapped lattice Hamiltonians recently discovered in three spatial dimensions, contain some “topological” features: They support fractional bulk excitations (dubbed fractons) and a ground-state degeneracy that is robust to local perturbations. However, because previous fracton models have been defined and analyzed only on a cubic lattice with periodic boundary conditions, it is unclear to what extent a notion of topology is applicable. In this paper, we demonstrate that the X-cube model, a prototypical type-I fracton model, can be defined on general three-dimensional manifolds. Our construction revolves around the notion of a singular compact total foliation of the spatial manifold, which constructs a lattice from intersecting stacks of parallel surfaces called leaves. We find that the ground-state degeneracy depends on the topology of the leaves and the pattern of leaf intersections. We further show that such a dependence can be understood from a renormalization group transformation for the X-cube model, wherein the system size can be changed by adding or removing 2D layers of topological states. Our results lead to an improved definition of fracton phase and bring to the fore the topological nature of fracton orders.Wilbur ShirleyKevin SlagleZhenghan WangXie ChenAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 8, Iss 3, p 031051 (2018)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Wilbur Shirley Kevin Slagle Zhenghan Wang Xie Chen Fracton Models on General Three-Dimensional Manifolds
description	Fracton models, a collection of exotic gapped lattice Hamiltonians recently discovered in three spatial dimensions, contain some “topological” features: They support fractional bulk excitations (dubbed fractons) and a ground-state degeneracy that is robust to local perturbations. However, because previous fracton models have been defined and analyzed only on a cubic lattice with periodic boundary conditions, it is unclear to what extent a notion of topology is applicable. In this paper, we demonstrate that the X-cube model, a prototypical type-I fracton model, can be defined on general three-dimensional manifolds. Our construction revolves around the notion of a singular compact total foliation of the spatial manifold, which constructs a lattice from intersecting stacks of parallel surfaces called leaves. We find that the ground-state degeneracy depends on the topology of the leaves and the pattern of leaf intersections. We further show that such a dependence can be understood from a renormalization group transformation for the X-cube model, wherein the system size can be changed by adding or removing 2D layers of topological states. Our results lead to an improved definition of fracton phase and bring to the fore the topological nature of fracton orders.
format	article
author	Wilbur Shirley Kevin Slagle Zhenghan Wang Xie Chen
author_facet	Wilbur Shirley Kevin Slagle Zhenghan Wang Xie Chen
author_sort	Wilbur Shirley
title	Fracton Models on General Three-Dimensional Manifolds
title_short	Fracton Models on General Three-Dimensional Manifolds
title_full	Fracton Models on General Three-Dimensional Manifolds
title_fullStr	Fracton Models on General Three-Dimensional Manifolds
title_full_unstemmed	Fracton Models on General Three-Dimensional Manifolds
title_sort	fracton models on general three-dimensional manifolds
publisher	American Physical Society
publishDate	2018
url	https://doaj.org/article/bff7eb400ebd4dd1bf6f77beadbfdc23
work_keys_str_mv	AT wilburshirley fractonmodelsongeneralthreedimensionalmanifolds AT kevinslagle fractonmodelsongeneralthreedimensionalmanifolds AT zhenghanwang fractonmodelsongeneralthreedimensionalmanifolds AT xiechen fractonmodelsongeneralthreedimensionalmanifolds
_version_	1718395366983860224

Fracton Models on General Three-Dimensional Manifolds

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