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Topological Defect Network Representations of Fracton Stabilizer Codes

Song, Zijian and Dua, Arpit and Shirley, Wilbur and Williamson, Dominic J. (2023) Topological Defect Network Representations of Fracton Stabilizer Codes. PRX Quantum, 4 (1). Art. No. 010304. ISSN 2691-3399. doi:10.1103/prxquantum.4.010304.

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A topological defect network (TDN) is formed by a network of topological defects embedded within a topological quantum field theory (TQFT). TDNs were introduced recently for the purpose of describing fracton topological phases of matter using the framework of defect TQFT. Their effectiveness has been demonstrated through numerous examples, yet a systematic construction was lacking. Here we solve this problem by formulating a method to construct TDNs for a wide range of lattice Hamiltonians. Our method takes a lattice Hamiltonian as input, applies an ungauging procedure, then creates a refined lattice within each unit cell, followed by regauging the system to produce a TDN as output. For topological Calderbank-Shor-Steane (CSS) Pauli stabilizer models, this procedure is guaranteed to produce a phase-equivalent TDN. This provides TDN representations of canonical fracton models for which no such construction was previously known, including Haah’s cubic code and Yoshida’s infinite family of fractal spin liquid models. We demonstrate the applicability of our method beyond CSS stabilizer models by constructing TDNs for non-CSS models including Chamon’s model and the semionic X-cube model.

Item Type:Article
Related URLs:
URLURL TypeDescription
Song, Zijian0000-0003-1044-4927
Dua, Arpit0000-0001-6348-4135
Williamson, Dominic J.0000-0002-8029-6408
Additional Information:A.D. acknowledges discussions with Meng Cheng, Qing-Rui Wang, and Kevin Slagle. D.W. acknowledges useful discussions with Daniel Bulmash and support from the Simons Foundation. A.D. and W.S. acknowledge support from the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (PHY-1733907) and from the Simons Collaboration on Ultra-Quantum Matter, which is a grant from the Simons Foundation (651438, AD; 651444, WS).
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Simons Foundation651438
Simons Foundation651444
Issue or Number:1
Record Number:CaltechAUTHORS:20230213-466022900.4
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:119236
Deposited By: Research Services Depository
Deposited On:24 Mar 2023 17:19
Last Modified:24 Mar 2023 20:37

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