Non-Liquid Cellular States

TL;DR

This paper introduces a generalized framework for constructing and analyzing non-liquid cellular quantum states, including non-abelian and higher-symmetry states, using topological, geometric, and cohomological methods within tensor networks.

Contribution

It develops a novel approach to build and understand non-liquid cellular states by gluing gauge-symmetry interfaces and incorporating higher-symmetry defects, extending existing topological theories.

Findings

Provides a construction mechanism for non-abelian non-liquid states.

Integrates gauge-symmetry-breaking and extension interfaces in cellular networks.

Connects topological quantum field theory data with tensor network analysis.

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.