# Anisotropic layer construction of anisotropic fracton models

## TL;DR

This paper introduces an anisotropic layered construction method for fracton topological orders in three dimensions, using coupled 2D topological layers, leading to novel quasiparticle behaviors constrained in subdimensional manifolds.

## Contribution

It presents a new coupled-layer approach to realize fracton phases, including exact solutions and generalizations to various 2D topological models.

## Key findings

- Exact solvable model in strong-coupling limit
- Fracton excitations from anyon pair condensation
- Generalized construction for multiple 2D topological models

## Abstract

We propose a coupled-layer construction of a class of fracton topological orders in three spatial dimensions, which is characterized by spatially anisotropic mobility of quasiparticle excitations constrained in subdimensional manifolds. The simplest model is obtained by stacking and coupling layers of the two-dimensional toric codes on the square lattice and can be exactly solved in the strong-coupling limit. The resulting fracton excitations are understood as a consequence of anyon pair condensation induced by the coupling between layers. We also present generalizations of the construction for layers of the Kitaev-honeycomb models, the $Z_N$ toric codes, and the toric codes and the doubled semion models on the honeycomb lattice.