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Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
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We introduce a generalization of conventional lattice gauge theory to describe fracton topological phases, which are characterized by immobile, point-like topological excitations, and sub-extensive topological degeneracy. We demonstrate a duality between fracton topological order and interacting spin systems with symmetries along extensive, lower-dimensional subsystems, which may be used to systematically search for and characterize fracton topological phases. Commutative algebra and elementary algebraic geometry provide an effective mathematical toolset for our results. Our work paves the way for identifying possible material realizations of fracton topological phases.
Forward citations
Cited by 11 Pith papers
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Fracton Topological Holography
Introduces FTH as an extension of TH/SymTFT to type-I and type-II fracton orders, demonstrating boundary switches and dualities for X-cube and Haah's code via stabilizer formalism.
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Mixed-state topological order and the errorfield double formulation of decoherence-induced transitions
Decoherence on abelian topological order is modeled as a temporal defect in double TQFT driving boundary anyon condensation transitions classified by Lagrangian subgroups of the doubled order.
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Nonadditivity in Quantum Field Theory: Replica Energies, Scaling Filters, and the Renormalization Group
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An algebraic RG formalism for topological orders uses ideals in fusion rings to encode noninvertible symmetries and condensation rules between anyons.
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A boundary-QFT analysis shows that curved bulk metrics create local edge velocities in topological models and that fracton and linearized-gravity theories carry Kac-Moody boundary algebras.
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Condensation of Magnetic Fluxes and Landscape of QCD Vacuum
The author exhibits sourceless Yang-Mills configurations with constant energy density and singular gauge potentials, and claims they are degenerate vacua separated by potential barriers.
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Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond
This review summarizes transformative examples of generalized symmetries in QFT and their applications to anomalies and dynamics.
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