Characterizing topological order by the information convex

TL;DR

This paper introduces the information convex, a new quantum information tool that characterizes bulk and boundary topological excitations in 2D topological orders, aiding in the detection and understanding of topological phases.

Contribution

The paper defines the information convex and demonstrates its ability to reveal and characterize bulk and boundary topological excitations in 2D topological orders, including non-Abelian quantum doubles.

Findings

Information convex encodes bulk anyons and gapped boundaries.

It reveals the condensation rules between bulk and boundary excitations.

Potential measurement methods via interference experiments in cold atoms.

Abstract

Motivated by previous efforts in detecting topological orders from the ground state(s) wave function, we introduce a new quantum information tool, coined the information convex, to capture the bulk and boundary topological excitations of a 2D topological order. Defined as a set of reduced density matrices that minimizes the energy in a subsystem, the information convex encodes not only the bulk anyons but also the gapped boundaries of 2D topological orders. Using untwisted gapped boundaries of non-Abelian quantum doubles as an example, we show how the information convex reveals and characterizes deconfined bulk and boundary topological excitations, and the condensation rule relating them. Interference experiments in cold atoms provide potential measurements for the invariant structure of information convex.