Characterizing topological order by the information convex

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.

37 pages, 26 figures, close to the published version

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• Twisted Quantum Double Model of Topological Phases in Two--Dimension
• A Family of Non-Abelian Kitaev Models on a Lattice: Topological Confinement and Condensation
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Cited by in corpus (14)

• Microscopic definitions of anyon data
• Entanglement Entropy, Quantum Fluctuations, and Thermal Entropy in Topological Phases
• Domain wall topological entanglement entropy
• Ishibashi States, Topological Orders with Boundaries and Topological Entanglement Entropy
• Seeing topological entanglement through the information convex
• Verlinde formula from entanglement
• Ishibashi States, Topological Orders with Boundaries and Topological Entanglement Entropy II -- Cutting through the boundary
• Exact description of the boundary theory of the Kitaev Toric Code with open boundary conditions
• An entropic invariant for 2D gapped quantum phases
• Correspondence between bulk entanglement and boundary excitation spectra in 2d gapped topological phases
• Boundary topological entanglement entropy in two and three dimensions
• Remote detectability from entanglement bootstrap I: Kirby's torus trick
• Immersed figure-8 annuli and anyons
• Knots and entanglement