Measuring Topological Order

TL;DR

This paper discusses methods to measure topological order in (2+1)D topological phases of matter by identifying invariant quantities and proposing experiments to determine their universal properties.

Contribution

It introduces physical experiments to measure topological invariants, linking experimental data to the universal properties of topological phases.

Findings

Identification of topologically invariant quantities

Proposed experiments to measure these invariants

Connection between measured data and topological order

Abstract

The topological order of a (2+1)D topological phase of matter is characterized by its chiral central charge and a unitary modular tensor category that describes the universal fusion and braiding properties of its anyonic quasiparticles. I discuss the topologically invariant quantities associated with these and identify ones that are useful for determining the topological order. I propose a variety of physical experiments that probe these quantities and detail the relation of the measured data to the topological invariants.