A higher-order non-uniform cellular automata algorithm is introduced for translationally invariant Euclidean and hyperbolic lattices, demonstrated on the {5,4} lattice to generate subsystem symmetry-protected topological states and simulate directed percolation.
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Gauging the 1-form symmetry in the X-Cube construction produces a web of relations to SPT phases with subsystem and higher-form symmetries plus subsystem symmetry fractionalization in the 3+1D toric code.
A dipole-conserving spin chain with Ising interactions stabilizes antiferromagnetic dipole order at the level of spin pairs and undergoes transitions to conventional antiferromagnetic or ferromagnetic order depending on interaction sign and strength.
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Universal Design and Physical Applications of Non-Uniform Cellular Automata on Translationally Invariant Lattices
A higher-order non-uniform cellular automata algorithm is introduced for translationally invariant Euclidean and hyperbolic lattices, demonstrated on the {5,4} lattice to generate subsystem symmetry-protected topological states and simulate directed percolation.
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There and Back Again: A Gauging Nexus between Topological and Fracton Phases
Gauging the 1-form symmetry in the X-Cube construction produces a web of relations to SPT phases with subsystem and higher-form symmetries plus subsystem symmetry fractionalization in the 3+1D toric code.
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Fractonic Constraints and Magnetic Order in a Dipole-Conserving Spin Chain
A dipole-conserving spin chain with Ising interactions stabilizes antiferromagnetic dipole order at the level of spin pairs and undergoes transitions to conventional antiferromagnetic or ferromagnetic order depending on interaction sign and strength.