Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries

Seifnashri, Sahand

doi:10.21468/SciPostPhys.16.4.098

Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries

Journal Article · Tue Apr 09 00:00:00 EDT 2024 · SciPost Physics

DOI:https://doi.org/10.21468/SciPostPhys.16.4.098· OSTI ID:2335823

We study ’t Hooft anomalies of global symmetries in 1+1d lattice Hamiltonian systems. We consider anomalies in internal and lattice translation symmetries. We derive a microscopic formula for the “anomaly cocycle” using topological defects implementing twisted boundary conditions. The anomaly takes value in the cohomology group H^3(G,U(1)) × H^2(G,U(1)) $H^{3} (G, U (1)) \times H^{2} (G, U (1))$ . The first factor captures the anomaly in the internal symmetry group G, and the second factor corresponds to a generalized Lieb-Schultz-Mattis anomaly involving G and lattice translation. We present a systematic procedure to gauge internal symmetries (that may not act on-site) on the lattice. We show that the anomaly cocycle is the obstruction to gauging the internal symmetry while preserving the lattice translation symmetry. As an application, we construct anomaly-free chiral lattice gauge theories. We demonstrate a one-to-one correspondence between (locality-preserving) symmetry operators and topological defects, which is essential for the results we prove. We also discuss the generalization to fermionic theories. Finally, we construct non-invertible lattice translation symmetries by gauging internal symmetries with a Lieb-Schultz-Mattis anomaly.

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Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0009988

OSTI ID:: 2335823

Alternate ID(s):: OSTI ID: 2580246

Journal Information:: SciPost Physics, Journal Name: SciPost Physics Journal Issue: 4 Vol. 16; ISSN 2542-4653

Publisher:: Stichting SciPostCopyright Statement

Country of Publication:: Netherlands

Language:: English

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Lieb-Schultz-Mattis anomalies and web of dualities induced by gauging in quantum spin chains Aksoy, Ömer Mert; Mudry, Christopher; Furusaki, Akira SciPost Physics, Vol. 16, Issue 1 https://doi.org/10.21468/SciPostPhys.16.1.022	journal	January 2024
Majorana chain and Ising model - (non-invertible) translations, anomalies, and emanant symmetries Seiberg, Nathan; Shao, Shu-Heng SciPost Physics, Vol. 16, Issue 3 https://doi.org/10.21468/SciPostPhys.16.3.064	journal	March 2024
On gauging finite subgroups Tachikawa, Yuji SciPost Physics, Vol. 8, Issue 1 https://doi.org/10.21468/SciPostPhys.8.1.015	journal	January 2020
Topological holography: Towards a unification of Landau and beyond-Landau physics Moradi, Heidar; Moosavian, Seyed Faroogh; Tiwari, Apoorv SciPost Physics Core, Vol. 6, Issue 4 https://doi.org/10.21468/SciPostPhysCore.6.4.066	journal	October 2023
A review of Quantum Cellular Automata Farrelly, Terry Quantum, Vol. 4 https://doi.org/10.22331/q-2020-11-30-368	journal	November 2020
Cohomology and Extensions of von Neumann Algebras, II Sutherland, Colin E. Publications of the Research Institute for Mathematical Sciences, Vol. 16, Issue 1 https://doi.org/10.2977/prims/1195187502	journal	April 1980
Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology Kapustin, Anton arXiv https://doi.org/10.48550/arXiv.1403.1467	preprint	January 2014
Anomalies of discrete symmetries in various dimensions and group cohomology Kapustin, Anton; Thorngren, Ryan arXiv https://doi.org/10.48550/arXiv.1404.3230	preprint	January 2014
Bosonic Topological Insulators and Paramagnets: a view from cobordisms Kapustin, Anton arXiv https://doi.org/10.48550/arXiv.1404.6659	preprint	January 2014
Short-range entanglement and invertible field theories Freed, Daniel S. arXiv https://doi.org/10.48550/arXiv.1406.7278	preprint	January 2014
Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases Thorngren, Ryan; Wang, Yifan arXiv https://doi.org/10.48550/arXiv.1912.02817	preprint	January 2019
Topological Defects on the Lattice: Dualities and Degeneracies Aasen, David; Fendley, Paul; Mong, Roger S. K. https://doi.org/10.48550/arXiv.2008.08598	posted_content	August 2020
The Lieb-Schultz-Mattis Theorem: A Topological Point of View Tasaki, Hal https://doi.org/10.48550/arXiv.2202.06243	journal	February 2022
Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond Cordova, Clay; Dumitrescu, Thomas T.; Intriligator, Kenneth arXiv https://doi.org/10.48550/arXiv.2205.09545	preprint	January 2022
Symmetry fractionalization, mixed-anomalies and dualities in quantum spin models with generalized symmetries Moradi, Heidar; Aksoy, Ömer M.; Bardarson, Jens H. arXiv https://doi.org/10.48550/arXiv.2307.01266	preprint	January 2023
Lieb-Schultz-Mattis theorem for 1d quantum magnets with antiunitary translation and inversion symmetries Yao, Yuan; Li, Linhao; Oshikawa, Masaki arXiv https://doi.org/10.48550/arXiv.2307.09843	preprint	January 2023
Anomalous symmetries of quantum spin chains and a generalization of the Lieb-Schultz-Mattis theorem Kapustin, Anton; Sopenko, Nikita arXiv https://doi.org/10.48550/arXiv.2401.02533	preprint	January 2024
Non-invertible symmetries and LSM-type constraints on a tensor product Hilbert space Seiberg, Nathan; Seifnashri, Sahand; Shao, Shu-Heng arXiv https://doi.org/10.48550/arXiv.2401.12281	preprint	January 2024
TASI 2003 Lectures on Anomalies Harvey, Jeffrey A. arXiv https://doi.org/10.48550/arXiv.hep-th/0509097	preprint	January 2005

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