Foliated BF theories and Multipole symmetries

Abstract

Due to the recent studies of the fracton topological phases, which host deconfined quasi-particle excitations with mobility restrictions, the concept of symmetries have been updated. Focusing on one of such new symmetries, multipole symmetries, including global, dipole, and quadruple symmetries, and gauge fields associated with them, we construct a new sets of ${\mathbb{Z}}_N$ $2+1d$ foliated BF theories, where BF theories of conventional topological phases are stacked in layers with couplings between them. By investigating gauge invariant non-local operators, we show that our foliated BF theories exhibit unusual ground state degeneracy depending on the system size; it depends on the greatest common divisor between $N$ and the system size. Our result provides a unified insight on UV lattice models of the fracton topological phases and other unconventional ones in view of foliated field theories.

22 pages, 5 figures

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Cited by in corpus (19)

• Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections
• Generating Lattice Non-invertible Symmetries
• (SPT-)LSM theorems from projective non-invertible symmetries
• Multipole and fracton topological order via gauging foliated SPT phases
• Anomaly inflow for dipole symmetry and higher form foliated field theories
• Topological order and Fractons from Gauging Exponential Symmetries
• Noninvertible operators in one, two, and three dimensions via gauging spatially modulated symmetry
• Anomaly inflow for CSS and fractonic lattice models and dualities via cluster state measurement
• Entanglement entropy of higher rank topological phases
• Generalized Modulated Symmetries in ${\mathbb{Z}}_2$ Topological Ordered Phases
• Spacetime symmetry-enriched SymTFT: from LSM anomalies to modulated symmetries and beyond
• Gauging Modulated Symmetries via Multiple Gauge Symmetry Operators and Adaptive Quantum Circuits
• Topological Dipole Insulator
• Infinite-component $BF$ field theory: Connection of fracton order, Toeplitz braiding, and non-Hermitian amplification
• There and Back Again: A Gauging Nexus between Topological and Fracton Phases
• ${\mathbb{Z}}_N$ generalizations of three-dimensional stabilizer codes
• Non-invertible translation from Lieb-Schultz-Mattis anomaly
• Matrix product state classification of 1D multipole symmetry protected topological phases
• Symmetry-enriched topological order and quasifractonic behavior in ${\mathbb{Z}}_N$ stabilizer codes