Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders

TL;DR

This paper introduces a systematic construction of exactly solvable 3D and 2D topological models using coupled quantum wires, enabling the study of both topological and fracton orders, including those with gapless surface states.

Contribution

It presents a new cellular construction method for coupled-wire models that can describe complex topological and fracton phases, including hybrid and chiral surface states.

Findings

Models describe both 3D topological and fracton orders.

Universal properties like quasiparticle statistics are analyzed.

Construction applies to 2D models with enriched topological orders.

Abstract

Three-dimensional (3D) gapped topological phases with fractional excitations are divided into two subclasses: one has topological order with point-like and loop-like excitations fully mobile in the 3D space, and the other has fracton order with point-like excitations constrained in lower-dimensional subspaces. These exotic phases are often studied by exactly solvable Hamiltonians made of commuting projectors, which, however, are not capable of describing those exhibiting surface states with gapless chiral dispersion. Here we introduce a systematic way, based on cellular construction recently proposed for 3D topological phases, to construct another type of exactly solvable models in terms of coupled quantum wires with given inputs of cellular structure, two-dimensional Abelian topological order, and their gapped interfaces. We show that our models can describe both 3D topological and fracton orders (and even their hybrid) and study their universal properties such as quasiparticle statistics and topological ground-state degeneracy. We also apply this construction to two-dimensional coupled-wire models with ordinary topological orders and translation-symmetry-enriched topological orders. Our results pave the way for effective quantum field theory descriptions or microscopic model realizations of fracton orders with chiral gapless surface states.