# Gauging fractons: immobile non-Abelian quasiparticles, fractals, and position-dependent degeneracies

## TL;DR

This paper introduces a new class of exactly solvable 3D lattice models that host immobile, non-Abelian quasiparticles with position-dependent degeneracies, expanding the understanding of fracton phases beyond traditional topological theories.

## Contribution

It develops a method to couple fracton models with topological quantum field theories, creating models with non-Abelian quasiparticles and fractal operator support, which are novel in the study of fracton phases.

## Key findings

- Hosts finite-energy non-Abelian immobile quasiparticles
- Degeneracies depend on quasiparticle positions and string geometry
- Provides exactly solvable models for fracton phases with non-Abelian excitations

## Abstract

The study of gapped quantum many-body systems in three spatial dimensions has uncovered the existence of quantum states hosting quasiparticles that are confined, not by energetics but by the structure of local operators, to move along lower dimensional submanifolds. These so-called "fracton" phases are beyond the usual topological quantum field theory description, and thus require new theoretical frameworks to describe them. Here we consider coupling fracton models to topological quantum field theories in (3+1) dimensions by starting with two copies of a known fracton model and gauging the $\mathbb{Z}_2$ symmetry that exchanges the two copies. This yields a class of exactly solvable lattice models that we study in detail for the case of the X-cube model and Haah's cubic code. The resulting phases host finite-energy non-Abelian immobile quasiparticles with robust degeneracies that depend on their relative positions. The phases also host non-Abelian string excitations with robust degeneracies that depend on the string geometry. Applying the construction to Haah's cubic code in particular provides an exactly solvable model with finite energy yet immobile non-Abelian quasiparticles that can only be created at the corners of operators with fractal support.