Zoo of quantum-topological phases of matter

TL;DR

This paper provides an accessible overview of topological phases of matter, highlighting their unique entanglement patterns and distinguishing between phases with and without topological order.

Contribution

It offers a simple introduction and survey of topological phases, clarifying the concepts of topological order and short-range entanglement in these phases.

Findings

Distinction between phases with long-range and short-range entanglement.

Explanation of topological order as a form of many-body entanglement.

Overview of the properties and significance of topological phases.

Abstract

What are topological phases of matter? First, they are phases of matter at zero temperature. Second, they have a non-zero energy gap for the excitations above the ground state. Third, they are disordered liquids that seem have no feature. But those disordered liquids actually can have rich patterns of many-body entanglement representing new kinds of order. This paper will give a simple introduction and a brief survey of topological phases of matter. We will first discuss topological phases that have topological order (ie with long range entanglement). Then we will cover topological phases that have no topological order (ie with only short-range entanglement).