Sufficient Conditions for Topological Order in Insulators

TL;DR

This paper establishes conditions under which insulating systems exhibit topological order by proving the existence of low energy excitations, offering a simplified proof of a recent theorem in higher dimensions.

Contribution

It provides a new, streamlined proof of the higher dimensional Lieb-Schultz-Mattis theorem and clarifies when low energy excitations can be considered topological in insulators.

Findings

Existence of low energy excitations in insulators under certain conditions

Identification of conditions for topological excitations

Simplified proof of the higher dimensional Lieb-Schultz-Mattis theorem

Abstract

We prove the existence of low energy excitations in insulating systems at general filling factor under certain conditions, and discuss in which cases these may be identified as topological excitations. This proof is based on previously proven locality results. In the case of half-filling it provides a significantly shortened proof of the recent higher dimensional Lieb-Schultz-Mattis theorem.