Twisted fracton models in three dimensions

Song, Hao; Prem, Abhinav; Huang, Sheng-Jie; Martin-Delgado, M. A.

doi:10.1103/physrevb.99.155118

Title: Twisted fracton models in three dimensions

Journal Article · Tue Apr 09 00:00:00 EDT 2019 · Physical Review B

DOI:https://doi.org/10.1103/physrevb.99.155118· OSTI ID:1612176

Song, Hao ^[1]; Prem, Abhinav ^[2]; Huang, Sheng-Jie ^[3]; Martin-Delgado, M. A. ^[1]

Univ. Complutense, Madrid (Spain)
Univ. of Colorado, Boulder, CO (United States); Princeton Univ., NJ (United States)
Univ. of Colorado, Boulder, CO (United States)

We study novel three-dimensional gapped quantum phases of matter which support quasiparticles with restricted mobility, including immobile “fracton” excitations. So far, most existing fracton models may be instructively viewed as generalized Abelian lattice gauge theories. Here, by analogy with Dijkgraaf-Witten topological gauge theories, we discover a natural generalization of fracton models, obtained by twisting the gauge symmetries. Introducing generalized gauge transformation operators carrying an extra phase factor depending on local configurations, we construct a plethora of exactly solvable three-dimensional models, which we dub “twisted fracton models.” A key result of our approach is to demonstrate the existence of rich non-Abelian fracton phases of distinct varieties in a three-dimensional system with finite-range interactions. For an accurate characterization of these novel phases, the notion of being inextricably non-Abelian is introduced for fractons and quasiparticles with one-dimensional mobility, referring to their new behavior of displaying braiding statistics that is, and remains, non-Abelian regardless of which quasiparticles with higher mobility are added to or removed from them. We also analyze these models by embedding them on a 3-torus and computing their ground-state degeneracies, which exhibit a surprising and novel dependence on the system size in the non-Abelian fracton phases. Furthermore, as an important advance in the study of fracton order, we develop a general mathematical framework which systematically captures the fusion and braiding properties of fractons and other quasiparticles with restricted mobility.

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Research Organization:: Univ. of Colorado, Boulder, CO (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0014415

OSTI ID:: 1612176

Alternate ID(s):: OSTI ID: 1505874

Journal Information:: Physical Review B, Vol. 99, Issue 15; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 39 works

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String-net condensation: A physical mechanism for topological phases Levin, Michael A.; Wen, Xiao-Gang arXiv https://doi.org/10.48550/arxiv.cond-mat/0404617	text	January 2004
Anyons in an exactly solved model and beyond Kitaev, Alexei arXiv https://doi.org/10.48550/arxiv.cond-mat/0506438	text	January 2005
Topological invariants of time-reversal-invariant band structures Moore, J. E.; Balents, L. arXiv https://doi.org/10.48550/arxiv.cond-mat/0607314	text	January 2006
Topological Insulators in Three Dimensions Fu, Liang; Kane, C. L.; Mele, E. J. arXiv https://doi.org/10.48550/arxiv.cond-mat/0607699	text	January 2006
Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells Bernevig, B. Andrei; Hughes, Taylor L.; Zhang, Shou-Cheng arXiv https://doi.org/10.48550/arxiv.cond-mat/0611399	text	January 2006
Quasi-Quantum Groups, Knots, Three-Manifolds, and Topological Field Theory Altschuler, Daniel; Coste, Antoine arXiv https://doi.org/10.48550/arxiv.hep-th/9202047	text	January 1992
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Ground-state degeneracy of non-Abelian topological phases from coupled wires Iadecola, Thomas; Neupert, Titus; Chamon, Claudio Physical Review B, Vol. 99, Issue 24 https://doi.org/10.1103/physrevb.99.245138	journal	June 2019
Building fracton phases by Majorana manipulation You, Yizhi; von Oppen, Felix Physical Review Research, Vol. 1, Issue 1 https://doi.org/10.1103/physrevresearch.1.013011	journal	August 2019
Foliated field theory and string-membrane-net condensation picture of fracton order Slagle, Kevin; Aasen, David; Williamson, Dominic SciPost Physics, Vol. 6, Issue 4 https://doi.org/10.21468/scipostphys.6.4.043	journal	January 2019
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Sorting topological stabilizer models in three dimensions Dua, Arpit; Kim, Isaac H.; Cheng, Meng Physical Review B, Vol. 100, Issue 15 https://doi.org/10.1103/physrevb.100.155137	journal	October 2019
Anisotropic layer construction of anisotropic fracton models Fuji, Yohei Physical Review B, Vol. 100, Issue 23 https://doi.org/10.1103/physrevb.100.235115	journal	December 2019
Ground-state degeneracy of non-Abelian topological phases from coupled wires Iadecola, Thomas; Neupert, Titus; Chamon, Claudio American Physical Society https://doi.org/10.5167/uzh-172138	text	January 2019
Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter Stephen, David T.; Nautrup, Hendrik Poulsen; Bermejo-Vega, Juani Quantum, Vol. 3 https://doi.org/10.22331/q-2019-05-20-142	journal	May 2019
Building fracton phases by Majorana manipulation You, Yizhi; Oppen, Felix Von Freie Universität Berlin https://doi.org/10.17169/refubium-26579	text	January 2019
Cage-Net Fracton Models Prem, Abhinav; Huang, Sheng-Jie; Song, Hao arXiv https://doi.org/10.48550/arxiv.1806.04687	text	January 2018
Entanglement Spectra of Stabilizer Codes: A Window into Gapped Quantum Phases of Matter Schmitz, Albert T.; Huang, Sheng-Jie; Prem, Abhinav arXiv https://doi.org/10.48550/arxiv.1901.10486	text	January 2019
Hyperbolic Fracton Model, Subsystem Symmetry, and Holography II: The Dual Eight-Vertex Model Yan, Han arXiv https://doi.org/10.48550/arxiv.1906.02305	text	January 2019
Electric Circuit Realizations of Fracton Physics Pretko, Michael arXiv https://doi.org/10.48550/arxiv.1908.08536	text	January 2019

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