Non-Liquid Cellular States

Abstract

The existence of quantum non-liquid states and fracton orders, both gapped and gapless states, challenges our understanding of phases of entangled matter. We generalize the cellular topological states to liquid or non-liquid cellular states. We propose a mechanism to construct more general non-abelian states by gluing gauge-symmetry-breaking vs gauge-symmetry-extension interfaces as extended defects in a cellular network, including defects of higher-symmetries, in any dimension. Our approach also naturally incorporates the anyonic particle/string condensations and composite string (related to particle-string or p-string)/membrane condensations. This approach shows gluing the familiar extended topological quantum field theory or conformal field theory data via topology, geometry, and renormalization consistency criteria (via certain modified group cohomology or cobordism theory data) in a tensor network can still guide us to analyze the non-liquid states. (Part of the abelian construction can be understood from the K-matrix Chern-Simons theory approach and the coupled-layer-by-junction constructions.) This approach may also lead us toward a unifying framework for quantum systems of both higher-symmetries and sub-system/sub-dimensional symmetries.

arXiv comment45 pages. Subtitle: Gluing Gauge-(Higher)-Symmetry-Breaking vs -Extension Interfacial Defects. This work relates to but also generalizes the construction in arXiv:2002.02433. v3: refinement and figures added. Accepted by Phys. Rev. Research

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• Long-range entanglement from measuring symmetry-protected topological phases
• Higher-Form Subsystem Symmetry Breaking: Subdimensional Criticality and Fracton Phase Transitions
• Optimal Thresholds for Fracton Codes and Random Spin Models with Subsystem Symmetry
• Fracton Self-Statistics
• Symmetric higher rank topological phases on generic graphs
• Designer non-Abelian fractons from topological layers
• Boundary Modes in the Chamon Model
• Hierarchy of Entanglement Renormalization and Long-Range Entangled States
• Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
• There and Back Again: A Gauging Nexus between Topological and Fracton Phases