Fracton Models on General Three-Dimensional Manifolds
By Wilbur E. Shirley, Kevin Slagle, Zhenghan Wang, Xie Chen. Physical Review X, 2017
166 citations recorded by the source corpus.
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 only been defined and analyzed 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.
Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/4b5b4a6bc22ca037a3b0ad72692a78593784a6e3
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In Atomic and Molecular Physics, and Optics
In Statistical and Nonlinear Physics
- M. Pretko
- M. Hermele
- R. Nandkishore
- Michael Jason Knap
- Frank Pollmann
- Tibor Rakovszky
- Yizhi You
- Xie Chen
Citations in the corpus
- Fracton phases of matter (2020, methodology): “[34] Wilbur Shirley, Kevin Slagle, Zhenghan Wang, and Xie Chen, “Fracton models on general three-dimensional manifolds,” Phys.”
- Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltonians (2019, background): “[53] Wilbur Shirley, Kevin Slagle, Zhenghan Wang, and Xie Chen, “Fracton models on general three-dimensional manifolds,” Phys.”
- Fractons (2018, methodology): “Since we have switched o↵ the term that would allow m’s to hop, we have three kinds of excitations with dynamics in our system: neutral composites, which, being fully mobile and created by local terms, are three-dimensional bosons; dim-2 excitations e((2)), which are two-dimensional bosons [38]; and”