Abstract
We classify subsystem symmetry-protected topological (SSPT) phases in $3+1$D protected by planar subsystem symmetries, which are dual to abelian fracton topological orders. We distinguish between weak SSPTs, which can be constructed by stacking $2+1$D SPTs, and strong SSPTs, which cannot. We identify signatures of strong phases, and show by explicit construction that such phases exist. A classification of strong phases is presented for an arbitrary finite abelian group. Finally, we show that fracton orders realizable via $p$-string condensation are dual to weak SSPTs, while strong SSPTs do not admit such a realization.
Highlights
Global symmetries, such as the Z2 spin-flip symmetry of the Ising model, act throughout the bulk of a system
We classify subsystem symmetry-protected topological (SSPT) phases in 3+1 dimensions (3+1D) protected by planar subsystem symmetries: short-range entangled phases which are dual to long-range entangled Abelian fracton topological orders via a generalized “gauging” duality
We explicitly construct strong subsystem SPT (SSPT) phases, which are dual to strong fracton phases with unusual braiding statistics that cannot be obtained by coupling 2D theories
Summary
Strong planar subsystem symmetry-protected topological phases and their dual fracton orders. Trithep Devakul Department of Physics, Princeton University, Princeton, New Jersey 08540, USA. Wilbur Shirley Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA. We classify subsystem symmetry-protected topological (SSPT) phases in 3+1 dimensions (3+1D) protected by planar subsystem symmetries: short-range entangled phases which are dual to long-range entangled Abelian fracton topological orders via a generalized “gauging” duality. We distinguish between weak SSPTs, which can be constructed by stacking 2+1D SPTs, and strong SSPTs, which cannot. We show that fracton orders realizable via p-string condensation are dual to weak SSPTs, while those dual to strong SSPTs exhibit statistical interactions prohibiting such a realization
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