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Fractionalization of subsystem symmetries in two dimensions

Stephen, David T. and Dua, Arpit and Garre-Rubio, José and Williamson, Dominic J. and Hermele, Michael (2022) Fractionalization of subsystem symmetries in two dimensions. Physical Review B, 106 (8). Art. No. 085104. ISSN 2469-9950. doi:10.1103/physrevb.106.085104.

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The fractionalization of global symmetry charges is a striking hallmark of topological quantum order. Here, we discuss the fractionalization of subsystem symmetries in two-dimensional topological phases. In line with previous no-go arguments, we show that subsystem symmetry fractionalization is not possible in many cases due to the additional rigid geometric structure of the symmetries. However, we identify a mechanism that allows fractionalization, involving global relations between macroscopically many symmetry generators. We find that anyons can fractionalize such relations, meaning that the total charge carried under all generators involved in the global relation is nontrivial, despite the fact that these generators multiply to the identity. We first discuss the general algebraic framework needed to characterize this type of fractionalization, and then explore this framework using a number of exactly solvable models with Z₂ topological order, including models having line and fractal symmetries. These models all showcase another necessary property of subsystem symmetry fractionalization: Fractionalized anyons must have restricted mobility when the symmetry is enforced, such that they are confined to a single line or point in the case of line and fractal symmetries, respectively. Looking forward, we expect that our identification of the importance of global relations in fractionalization will hold significance for the classification of phases with subsystem symmetries in all dimensions.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Stephen, David T.0000-0002-3150-0169
Garre-Rubio, José0000-0003-1845-7554
Williamson, Dominic J.0000-0002-8029-6408
Additional Information:© 2022 American Physical Society. (Received 7 April 2022; revised 28 June 2022; accepted 22 July 2022; published 3 August 2022) D.T.S. thanks M. Qi for helpful discussions. The research of M.H. is supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award No. DE-SC0014415. This work was also partly supported by the Simons Collaboration on Ultra-Quantum Matter, which is a Gant from the Simons Foundation (651440, M.H., D.T.S.; 651438, A.D.), and the Simons Collaboration on It from Qubit (D.J.W.). The work of M.H. on the general framework for subsystem symmetry fractionalization and on models with a pair of line symmetries (Secs. II and III) was supported by the DOE BES project, while his work on models with three line symmetries and fractal symmetries (Secs. IV and V) was supported by the Simons Foundation. It was also supported by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (Grant No. PHY-1733907, A.D.). J.G.R. has been partially supported by the ERC under the European Union's Horizon 2020 research and innovation programme through the ERC-CoG SEQUAM (Grant Agreement No. 863476).
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0014415
Simons Foundation651440
Simons Foundation651438
European Research Council (ERC)863476
Issue or Number:8
Record Number:CaltechAUTHORS:20220803-536016000
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:116075
Deposited By: George Porter
Deposited On:04 Aug 2022 19:41
Last Modified:04 Aug 2022 19:41

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