Comments on foliated gauge theories and dualities in 3+1d

Hsin, Po-Shen; Slagle, Kevin

doi:10.21468/SciPostPhys.11.2.032

Title: Comments on foliated gauge theories and dualities in 3+1d

Journal Article · Tue Aug 17 00:00:00 EDT 2021 · SciPost Physics

DOI:https://doi.org/10.21468/SciPostPhys.11.2.032· OSTI ID:1813626

Hsin, Po-Shen ^[1]; Slagle, Kevin ^[2]

Walter Burke Institute for Theoretical Physics
California Institute of Technology, Walter Burke Institute for Theoretical Physics

We investigate the properties of foliated gauge fields and construct several foliated field theories in 3+1d that describe foliated fracton orders both with and without matter, including the recent hybrid fracton models. These field theories describe Abelian or non-Abelian gauge theories coupled to foliated gauge fields, and they fall into two classes of models that we call the electric models and the magnetic models. We show that these two classes of foliated field theories enjoy a duality. We also construct a model (using foliated gauge fields and an exactly solvable lattice Hamiltonian model) for a subsystem-symmetry protected topological (SSPT) phase, which is analogous to a one-form symmetry protected topological phase, with the subsystem symmetry acting on codimension-two subregions. We construct the corresponding gauged SSPT phase as a foliated two-form gauge theory. Some instances of the gauged SSPT phase are a variant of the X-cube model with the same ground state degeneracy and the same fusion, but different particle statistics.

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Research Organization:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP); Simons Foundation; Walter Burke Institute for Theoretical Physics

Grant/Contract Number:: SC0011632

OSTI ID:: 1813626

Alternate ID(s):: OSTI ID: 1851501

Journal Information:: SciPost Physics, Journal Name: SciPost Physics Vol. 11 Journal Issue: 2; ISSN 2542-4653

Publisher:: Stichting SciPostCopyright Statement

Country of Publication:: Netherlands

Language:: English

References (51)

A new kind of topological quantum order: A dimensional hierarchy of quasiparticles built from stationary excitations Vijay, Sagar; Haah, Jeongwan; Fu, Liang Physical Review B, Vol. 92, Issue 23 https://doi.org/10.1103/PhysRevB.92.235136	journal	December 2015
On 2-group global symmetries and their anomalies Benini, Francesco; Córdova, Clay; Hsin, Po-Shen Journal of High Energy Physics, Vol. 2019, Issue 3 https://doi.org/10.1007/JHEP03(2019)118	journal	March 2019
Three-dimensional topological lattice models with surface anyons von Keyserlingk, C. W.; Burnell, F. J.; Simon, S. H. Physical Review B, Vol. 87, Issue 4 https://doi.org/10.1103/PhysRevB.87.045107	journal	January 2013
Fractional excitations in foliated fracton phases Shirley, Wilbur; Slagle, Kevin; Chen, Xie Annals of Physics, Vol. 410 https://doi.org/10.1016/j.aop.2019.167922	journal	November 2019
Comments on one-form global symmetries and their gauging in 3d and 4d Hsin, Po-Shen; Lam, Ho Tat; Seiberg, Nathan SciPost Physics, Vol. 6, Issue 3 https://doi.org/10.21468/SciPostPhys.6.3.039	journal	January 2019
Quantum Glassiness in Strongly Correlated Clean Systems: An Example of Topological Overprotection Chamon, Claudio Physical Review Letters, Vol. 94, Issue 4 https://doi.org/10.1103/PhysRevLett.94.040402	journal	January 2005
Glassy quantum dynamics in translation invariant fracton models Prem, Abhinav; Haah, Jeongwan; Nandkishore, Rahul Physical Review B, Vol. 95, Issue 15 https://doi.org/10.1103/PhysRevB.95.155133	journal	April 2017
More exotic field theories in 3+1 dimensions Gorantla, Pranay; Lam, Ho Tat; Seiberg, Nathan SciPost Physics, Vol. 9, Issue 5 https://doi.org/10.21468/SciPostPhys.9.5.073	journal	January 2020
Topological color code and symmetry-protected topological phases Yoshida, Beni Physical Review B, Vol. 91, Issue 24 https://doi.org/10.1103/PhysRevB.91.245131	journal	June 2015
Standard form of qudit stabilizer groups Gheorghiu, Vlad Physics Letters A, Vol. 378, Issue 5-6 https://doi.org/10.1016/j.physleta.2013.12.009	journal	January 2014
Generalized global symmetries Gaiotto, Davide; Kapustin, Anton; Seiberg, Nathan Journal of High Energy Physics, Vol. 2015, Issue 2 https://doi.org/10.1007/JHEP02(2015)172	journal	February 2015
Exotic $\mathbb{Z}_N$ symmetries, duality, and fractons in 3+1-dimensional quantum field theory Seiberg, Nathan; Shao, Shu-Heng SciPost Physics, Vol. 10, Issue 1 https://doi.org/10.21468/SciPostPhys.10.1.003	journal	January 2021
Local stabilizer codes in three dimensions without string logical operators Haah, Jeongwan Physical Review A, Vol. 83, Issue 4 https://doi.org/10.1103/PhysRevA.83.042330	journal	April 2011
Braiding statistics and link invariants of bosonic/fermionic topological quantum matter in 2+1 and 3+1 dimensions Putrov, Pavel; Wang, Juven; Yau, Shing-Tung Annals of Physics, Vol. 384 https://doi.org/10.1016/j.aop.2017.06.019	journal	September 2017
Time-reversal breaking in QCD4, walls, and dualities in 2 + 1 dimensions Gaiotto, Davide; Komargodski, Zohar; Seiberg, Nathan Journal of High Energy Physics, Vol. 2018, Issue 1 https://doi.org/10.1007/JHEP01(2018)110	journal	January 2018
Subsystem symmetry protected topological order You, Yizhi; Devakul, Trithep; Burnell, F. J. Physical Review B, Vol. 98, Issue 3 https://doi.org/10.1103/PhysRevB.98.035112	journal	July 2018
Fracton topological order from the Higgs and partial-confinement mechanisms of rank-two gauge theory Ma, Han; Hermele, Michael; Chen, Xie Physical Review B, Vol. 98, Issue 3 https://doi.org/10.1103/PhysRevB.98.035111	journal	July 2018
Hybrid fracton phases: Parent orders for liquid and nonliquid quantum phases Tantivasadakarn, Nathanan; Ji, Wenjie; Vijay, Sagar Physical Review B, Vol. 103, Issue 24 https://doi.org/10.1103/PhysRevB.103.245136	journal	June 2021
Fracton physics of spatially extended excitations Li, Meng-Yuan; Ye, Peng Physical Review B, Vol. 101, Issue 24 https://doi.org/10.1103/PhysRevB.101.245134	journal	June 2020
Symmetric fracton matter: Twisted and enriched You, Yizhi; Devakul, Trithep; Burnell, F. J. Annals of Physics, Vol. 416 https://doi.org/10.1016/j.aop.2020.168140	journal	May 2020
Topological field theory on a lattice, discrete theta-angles and confinement Kapustin, Anton; Thorngren, Ryan Advances in Theoretical and Mathematical Physics, Vol. 18, Issue 5 https://doi.org/10.4310/ATMP.2014.v18.n5.a4	journal	January 2014
Quantum Self-Correction in the 3D Cubic Code Model Bravyi, Sergey; Haah, Jeongwan Physical Review Letters, Vol. 111, Issue 20 https://doi.org/10.1103/PhysRevLett.111.200501	journal	November 2013
Topological defect networks for fractons of all types Aasen, David; Bulmash, Daniel; Prem, Abhinav Physical Review Research, Vol. 2, Issue 4 https://doi.org/10.1103/PhysRevResearch.2.043165	journal	October 2020
Braiding Statistics of Loop Excitations in Three Dimensions Wang, Chenjie; Levin, Michael Physical Review Letters, Vol. 113, Issue 8 https://doi.org/10.1103/PhysRevLett.113.080403	journal	August 2014
Quantum memories at finite temperature Brown, Benjamin J.; Loss, Daniel; Pachos, Jiannis K. Reviews of Modern Physics, Vol. 88, Issue 4 https://doi.org/10.1103/RevModPhys.88.045005	journal	November 2016
Fractonic Chern-Simons and BF theories You, Yizhi; Devakul, Trithep; Sondhi, S. L. Physical Review Research, Vol. 2, Issue 2 https://doi.org/10.1103/PhysRevResearch.2.023249	journal	May 2020
Coupling a QFT to a TQFT and duality Kapustin, Anton; Seiberg, Nathan Journal of High Energy Physics, Vol. 2014, Issue 4 https://doi.org/10.1007/JHEP04(2014)001	journal	April 2014
Fracton topological order via coupled layers Ma, Han; Lake, Ethan; Chen, Xie Physical Review B, Vol. 95, Issue 24 https://doi.org/10.1103/PhysRevB.95.245126	journal	June 2017
Quantum field theory of X-cube fracton topological order and robust degeneracy from geometry Slagle, Kevin; Kim, Yong Baek Physical Review B, Vol. 96, Issue 19 https://doi.org/10.1103/PhysRevB.96.195139	journal	November 2017
Fracton fusion and statistics Pai, Shriya; Hermele, Michael Physical Review B, Vol. 100, Issue 19 https://doi.org/10.1103/PhysRevB.100.195136	journal	November 2019
Lattice models that realize $Z_{n}$ -1 symmetry-protected topological states for even $n$ Tsui, Lokman; Wen, Xiao-Gang Physical Review B, Vol. 101, Issue 3 https://doi.org/10.1103/PhysRevB.101.035101	journal	January 2020
Symmetry-enriched quantum spin liquids in (3 + 1)d Hsin, Po-Shen; Turzillo, Alex Journal of High Energy Physics, Vol. 2020, Issue 9 https://doi.org/10.1007/JHEP09(2020)022	journal	September 2020
Fracton topological order, generalized lattice gauge theory, and duality Vijay, Sagar; Haah, Jeongwan; Fu, Liang Physical Review B, Vol. 94, Issue 23 https://doi.org/10.1103/PhysRevB.94.235157	journal	December 2016
Higher-rank tensor field theory of non-abelian fracton and embeddon Wang, Juven; Xu, Kai Annals of Physics, Vol. 424 https://doi.org/10.1016/j.aop.2020.168370	journal	January 2021
Twisted foliated fracton phases Shirley, Wilbur; Slagle, Kevin; Chen, Xie Physical Review B, Vol. 102, Issue 11 https://doi.org/10.1103/PhysRevB.102.115103	journal	September 2020
Classification of subsystem symmetry-protected topological phases Devakul, Trithep; Williamson, Dominic J.; You, Yizhi Physical Review B, Vol. 98, Issue 23 https://doi.org/10.1103/PhysRevB.98.235121	journal	December 2018
Higgs mechanism in higher-rank symmetric U(1) gauge theories Bulmash, Daniel; Barkeshli, Maissam Physical Review B, Vol. 97, Issue 23 https://doi.org/10.1103/PhysRevB.97.235112	journal	June 2018
Fracton Models on General Three-Dimensional Manifolds Shirley, Wilbur; Slagle, Kevin; Wang, Zhenghan Physical Review X, Vol. 8, Issue 3 https://doi.org/10.1103/PhysRevX.8.031051	journal	August 2018
Comments on global symmetries, anomalies, and duality in (2 + 1)d Benini, Francesco; Hsin, Po-Shen; Seiberg, Nathan Journal of High Energy Physics, Vol. 2017, Issue 4 https://doi.org/10.1007/JHEP04(2017)135	journal	April 2017
Subdimensional particle structure of higher rank $U (1)$ spin liquids Pretko, Michael Physical Review B, Vol. 95, Issue 11 https://doi.org/10.1103/PhysRevB.95.115139	journal	March 2017
Spin TQFTs and fermionic phases of matter Gaiotto, Davide; Kapustin, Anton International Journal of Modern Physics A, Vol. 31, Issue 28n29 https://doi.org/10.1142/S0217751X16450445	journal	October 2016
The fracton gauge principle Pretko, Michael Physical Review B, Vol. 98, Issue 11 https://doi.org/10.1103/PhysRevB.98.115134	journal	September 2018
Universal entanglement signatures of foliated fracton phases Shirley, Wilbur; Slagle, Kevin; Chen, Xie SciPost Physics, Vol. 6, Issue 1 https://doi.org/10.21468/SciPostPhys.6.1.015	journal	January 2019
Exotic $U(1)$ symmetries, duality, and fractons in 3+1-dimensional quantum field theory Seiberg, Nathan; Shao, Shu-Heng SciPost Physics, Vol. 9, Issue 4 https://doi.org/10.21468/SciPostPhys.9.4.046	journal	January 2020
Fault-tolerant quantum computation by anyons Kitaev, A. Yu. Annals of Physics, Vol. 303, Issue 1 https://doi.org/10.1016/S0003-4916(02)00018-0	journal	January 2003
Fracton phases via exotic higher-form symmetry-breaking Qi, Marvin; Radzihovsky, Leo; Hermele, Michael Annals of Physics, Vol. 424 https://doi.org/10.1016/j.aop.2020.168360	journal	January 2021
Fracton phases of matter Pretko, Michael; Chen, Xie; You, Yizhi International Journal of Modern Physics A, Vol. 35, Issue 06 https://doi.org/10.1142/S0217751X20300033	journal	February 2020
Foliated Quantum Field Theory of Fracton Order Slagle, Kevin Physical Review Letters, Vol. 126, Issue 10 https://doi.org/10.1103/PhysRevLett.126.101603	journal	March 2021
Exotic symmetries, duality, and fractons in 2+1-dimensional quantum field theory Seiberg, Nathan; Shao, Shu-Heng SciPost Physics, Vol. 10, Issue 2 https://doi.org/10.21468/SciPostPhys.10.2.027	journal	January 2021
Fractons Nandkishore, Rahul M.; Hermele, Michael Annual Review of Condensed Matter Physics, Vol. 10, Issue 1 https://doi.org/10.1146/annurev-conmatphys-031218-013604	journal	March 2019
Foliated fracton order from gauging subsystem symmetries Shirley, Wilbur; Slagle, Kevin; Chen, Xie SciPost Physics, Vol. 6, Issue 4 https://doi.org/10.21468/SciPostPhys.6.4.041	journal	January 2019

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