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Lieb-Schultz-Mattis anomalies and web of dualities induced by gauging in quantum spin chains
CMT Group, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland.
CMT Group, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland; Institut de Physique, EPF Lausanne, CH-1015 Lausanne, Switzerland.
RIKEN Center for Emergent Matter Science, Wako, Saitama, 351-0198, Japan, Saitama; Condensed Matter Theory Laboratory, RIKEN, Wako, Saitama, 351-0198, Japan.
KTH, Skolan för teknikvetenskap (SCI), Fysik, Kondenserade materiens teori.ORCID-id: 0000-0003-4742-775X
2024 (engelsk)Inngår i: SciPost Physics, E-ISSN 2542-4653, Vol. 16, nr 1, artikkel-id 022Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

Lieb-Schultz-Mattis (LSM) theorems impose non-perturbative constraints on the zero-temperature phase diagrams of quantum lattice Hamiltonians (always assumed to be local in this paper). LSM theorems have recently been interpreted as the lattice counterparts to mixed 't Hooft anomalies in quantum field theories that arise from a combination of crystalline and global internal symmetry groups. Accordingly, LSM theorems have been reinterpreted as LSM anomalies. In this work, we provide a systematic diagnostic for LSM anomalies in one spatial dimension. We show that gauging subgroups of the global internal symmetry group of a quantum lattice model obeying an LSM anomaly delivers a dual quantum lattice Hamiltonian such that its internal and crystalline symmetries mix non-trivially through a group extension. This mixing of crystalline and internal symmetries after gauging is a direct consequence of the LSM anomaly, i.e., it can be used as a diagnostic of an LSM anomaly. We exemplify this procedure for a quantum spin-1/2 chain obeying an LSM anomaly resulting from combining a global internal Z2×Z2 symmetry with translation or reflection symmetry. We establish a triality of models by gauging a Z2⊂Z2×Z2 symmetry in two ways, one of which amounts to performing a Kramers-Wannier duality, while the other implements a Jordan-Wigner duality. We discuss the mapping of the phase diagram of the quantum spin-1/2 XYZ chains under such a triality. We show that the deconfined quantum critical transitions between Neel and dimer orders are mapped to either topological or conventional Landau-Ginzburg transitions. Finally, we extend our results to Zn clock models with Zn×Zn global internal symmetry, and provide a reinterpretation of the dual internal symmetries in terms of Zn charge and dipole symmetries

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Stichting SciPost , 2024. Vol. 16, nr 1, artikkel-id 022
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URN: urn:nbn:se:kth:diva-367426DOI: 10.21468/SciPostPhys.16.1.022ISI: 001166003200002Scopus ID: 2-s2.0-85190722017OAI: oai:DiVA.org:kth-367426DiVA, id: diva2:1984833
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QC 20250718

Tilgjengelig fra: 2025-07-18 Laget: 2025-07-18 Sist oppdatert: 2025-07-18bibliografisk kontrollert

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