Symmetric higher rank topological phases on generic graphs

Abstract

Motivated by recent interests in fracton topological phases, we explore the interplay between gapped 2D ${\mathbb{Z}}_N$ topological phases which admit fractional excitations with restricted mobility and geometry of the lattice on which such phases are placed. We investigate the properties of the phases in a new geometric context -- graph theory. By placing the phases on a 2D lattice consisting of two arbitrary connected graphs, $G_x⊠G_y$, we study the behavior of fractional excitations of the phases. We derive the formula of the ground state degeneracy of the phases, which depends on invariant factors of the Laplacian.

25 pages, 6 figures

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• Anomaly inflow for dipole symmetry and higher form foliated field theories
• Unveiling UV/IR Mixing via Symmetry Defects: A View from Topological Entanglement Entropy
• Generalized Modulated Symmetries in ${\mathbb{Z}}_2$ Topological Ordered Phases
• Entanglement entropy of higher rank topological phases
• Gauging Modulated Symmetries via Multiple Gauge Symmetry Operators and Adaptive Quantum Circuits
• Spacetime symmetry-enriched SymTFT: from LSM anomalies to modulated symmetries and beyond