Multipole and fracton topological order via gauging foliated SPT phases

Abstract

Spurred by recent development of fracton topological phases, unusual topological phases possessing fractionalized quasi-particles with mobility constraints, the concept of symmetries has been renewed. In particular, in accordance with the progress of multipole symmetries, associated with conservation of multipoles, such as dipole or quadruple moments as well as global charges, there have been proposed topological phases with such symmetries. These topological phases are unconventional as excitations are subject to mobility constraints corresponding to the multipole symmetries. We demonstrate a way to construct such phases by preparing layers of symmetry protected topological (SPT) phases and implementing gauging a global symmetry. After gauging, the statistics of a fractional excitation is altered when crossing the SPT phases, resulting in topological phases with the multipole symmetries. The way we construct the phases allows us to have a comprehensive understanding of field theories of topological phases with the multipole symmetries and other fracton models.

28 pages, 6 figures

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• Symmetric higher rank topological phases on generic graphs
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• Scalar, fermionic and supersymmetric field theories with subsystem symmetries in d+1 dimensions

Cited by in corpus (11)

• (SPT-)LSM theorems from projective non-invertible symmetries
• Anomaly inflow for dipole symmetry and higher form foliated field theories
• 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
• Spacetime symmetry-enriched SymTFT: from LSM anomalies to modulated symmetries and beyond
• Gauging Modulated Symmetries via Multiple Gauge Symmetry Operators and Adaptive Quantum Circuits
• There and Back Again: A Gauging Nexus between Topological and Fracton Phases
• Matrix product state classification of 1D multipole symmetry protected topological phases
• Symmetry-enriched topological order and quasifractonic behavior in ${\mathbb{Z}}_N$ stabilizer codes
• Non-invertible translation from Lieb-Schultz-Mattis anomaly