# Haah codes on general three manifolds

## TL;DR

This paper proposes a framework to generalize Haah codes, a type of fracton model, to all 3-manifolds using Hastings' LR stabilizer codes, aiming to extend their topological quantum field theory description.

## Contribution

It introduces a new approach to extend Haah codes to arbitrary 3-manifolds leveraging Hastings' LR stabilizer codes for finite groups.

## Key findings

- Outline of a program for generalization to all 3-manifolds
- Connection to topological quantum field theory frameworks
- Potential for broader applicability of fracton models

## Abstract

Haah codes represent a singularly interesting gapped Hamiltonian schema that has resisted a natural generalization, although recent work shows that the closely related type I fracton models are more commonplace. These type I siblings of Haah codes are better understood, and a generalized topological quantum field theory framework has been proposed. Following the same conceptual framework, we outline a program to generalize Haah codes to all 3-manifolds using Hastings' LR stabilizer codes for finite groups.