# Fracton Topological Order from Nearest-Neighbor Two-Spin Interactions and Dualities

## TL;DR

This paper introduces a realistic 3D lattice model with only nearest-neighbor two-spin interactions that exhibits fracton topological order, making it more feasible for experimental realization.

## Contribution

The authors present a new 3D lattice model with only two-spin interactions that realizes X-cube fracton order, derived from coupled Kitaev honeycomb layers, and analyze its phase transitions.

## Key findings

- Model exhibits X-cube fracton topological order with simple interactions.
- Includes dual descriptions of quantum phase transitions.
- Demonstrates first-order nature of phase transitions.

## Abstract

Fracton topological order describes a remarkable phase of matter which can be characterized by fracton excitations with constrained dynamics and a ground state degeneracy that increases exponentially with the length of the system on a three-dimensional torus. However, previous models exhibiting this order require many-spin interactions which may be very difficult to realize in a real material or cold atom system. In this work, we present a more physically realistic model which has the so-called X-cube fracton topological order but only requires nearest-neighbor two-spin interactions. The model lives on a three-dimensional honeycomb-based lattice with one to two spin-1/2 degrees of freedom on each site and a unit cell of 6 sites. The model is constructed from two orthogonal stacks of $Z_2$ topologically ordered Kitaev honeycomb layers, which are coupled together by a two-spin interaction. It is also shown that a four-spin interaction can be included to instead stabilize 3+1D $Z_2$ topological order. We also find dual descriptions of four quantum phase transitions in our model, all of which appear to be discontinuous first order transitions.