2020/07/31 by Chao‐Ming Jian, Chao-Ming Jian, Cenke Xu
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Anomaly (physics) #Compactification (mathematics) #Geometry #Global symmetry #Homogeneous space #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum mechanics #Quantum, superfluid, helium dynamics #Spontaneous symmetry breaking #Symmetry (geometry) #Symmetry breaking #Theoretical physics #Topological Materials and Phenomena #Topology (electrical circuits) #cond-mat.str-el
paper · pdf · doi:10.1088/1742-5468/abe411
published as J. Stat. Mech. (2021) 033102 · 13 pages
arxiv created 2021/01/19 · openalex publication_date 2021/03/01 · arxiv updated 2021/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Abstract We consider quantum many body systems with generalized symmetries, such as the higher form symmetries introduced recently, and the ‘tensor symmetry’. We consider a general form of lattice Hamiltonians which allow a certain level of nonlocality. Based on the assumption of dual generalized symmetries, we explicitly construct low energy excited states. We also derive the ’t Hooft anomaly for the general Hamiltonians after ‘gauging’ the dual generalized symmetries. A 3d system with dual anomalous 1-form symmetries can be viewed as the boundary of a 4d generalized symmetry protected topological (SPT) state with 1-form symmetries. We also present a prototype example of a 4d SPT state with mixed 1-form and 0-form symmetry topological response theory as well as its physical construction. The boundary of this SPT state can be a 3d anomalous QED state, or an anomalous 1-form symmetry-enriched topological order. Insights are gained by dimensional compatification/reduction. After dimensional compactification, the 3d system with N pairs of dual 1-form symmetries reduces to a 1d system with 2 N pairs of dual U(1) global symmetries, which is the boundary of an ordinary 2d SPT state, while the 3d system with tensor symmetry reduces to a 1d Lifshitz theory, which is protected by the center of mass conservation of the system.