A Topological Phase in a Quantum Gravity Model

TL;DR

This paper discusses the challenges in defining topological phases, proposes a flexible approach, and identifies potential topological phases within a class of quantum gravity models that are neither lattice nor field theoretic.

Contribution

It introduces a simple class of quantum gravity models that may contain candidates for topological phases, highlighting the need for flexible definitions.

Findings

Identification of candidate topological phases in quantum gravity models

Discussion on the importance of flexible definitions of topological phases

Analysis of strengths and weaknesses of various definitions

Abstract

I would claim that we do not have a suitably general definition of what a topological phase is, or more importantly, any robust understanding of how to enter one even in the world of mathematical models. The latter is, of course, the more important issue and the main subject of this note. But a good definition can sharpen our thinking and a poor definition can misdirect us. I will not attempt a final answer here but merely comment on the strengths and weaknesses of possible definitions and argue for some flexibility. In particular, I describe a rather simple class of ``quantum gravity'' models which are neither lattice nor field theoretic but appear to contain strong candidates for topological phases.