Lattice Clifford fractons and their Chern-Simons-like theory

Abstract

We use Dirac matrix representations of the Clifford algebra to build fracton models on the lattice and their effective Chern-Simons-like theory. As an example we build lattice fractons in odd $D$ spatial dimensions and their $(D+1)$ effective theory. The model possesses an anti-symmetric $K$ matrix resembling that of hierarchical quantum Hall states. The gauge charges are conserved in sub-dimensional manifolds which ensures the fractonic behavior. The construction extends to any lattice fracton model built from commuting projectors and with tensor products of spin-$1/2$ degrees of freedom at the sites.

50 pages, 3 figures, few comments added

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• Rank-2 Toric Code in Two Dimensions
• Effective Fractonic Behavior in a Two-Dimensional Exactly Solvable Spin Liquid
• Realization of fractonic quantum phases in the breathing pyrochlore lattice
• Boundary Modes in the Chamon Model
• Spectroscopic fingerprints of gapless type-II fracton phases
• Fractal Subsystem Symmetries, 't Hooft Anomalies, and UV/IR Mixing
• The spin-orbital Kitaev model: from kagome spin ice to classical fractons
• Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
• Fractonic criticality in Rydberg atom arrays
• Field Theories for type-II fractons