Type-II fractons from coupled spin chains and layers

TL;DR

This paper presents a novel method to construct various topological orders, including fracton types, from coupled lower-dimensional systems, providing new insights into their structure and relationships.

Contribution

It introduces coupled spin chain and layer constructions for generating both conventional and fracton topological orders, including Haah's cubic code and Yoshida's fractal spin liquids.

Findings

Constructed Haah's cubic code from coupled spin chains.

Developed layered approach for Yoshida's fractal spin liquids.

Unified framework for topological orders from lower-dimensional systems.

Abstract

We describe a construction of topological orders from coupled lower dimensional symmetry-protected topological orders, which is closely related to gauging a subsystem symmetry. Our construction yields both conventional topological orders and exotic fracton topological orders of type-I and type-II. In particular, we find a coupled spin chain construction of Haah's cubic code, and a coupled layer construction of Yoshida's fractal spin liquids.