Topological entanglement entropy meets holographic entropy inequalities

Abstract

Topological entanglement entropy (TEE) is an efficient way to detect topological order in the ground state of gapped Hamiltonians. The seminal work of Kitaev and Preskill~\cite{preskill-kitaev-tee} and simultaneously by Levin and Wen~\cite{levin-wen-tee} proposed information quantities that can probe the TEE. In the present work, we explain why the subtraction schemes in the proposed information quantities~\cite{levin-wen-tee,preskill-kitaev-tee} work for the computation of TEE and generalize them for arbitrary number of subregions by explicitly noting the necessary conditions for an information quantity to capture TEE. Our conditions differentiate the probes defined by Kitaev-Preskill and Levin-Wen into separate classes. While there are infinitely many possible probes of TEE, we focus particularly on the cyclic quantities $Q_{2n+1}$ and multi-information $I_n$. We also show that the holographic entropy inequalities are satisfied by the quantum entanglement entropy of the non-degenerate ground state of a topologically ordered two-dimensional medium with a mass gap.

arXiv commentv1 9+4 pages, 3+2 figures; v2 9+7 pages, typos corrected, appendix added

References in corpus (34)

• Non-Abelian Anyons and Topological Quantum Computation
• Anyons in an exactly solved model and beyond
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Area laws for the entanglement entropy - a review
• New directions in the pursuit of Majorana fermions in solid state systems
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Aspects of Holographic Entanglement Entropy
• Entropy and Area
• Direct observation of anyonic braiding statistics at the $\nu$=1/3 fractional quantum Hall state
• Fractional statistics in anyon collisions
• A finite entanglement entropy and the c-theorem
• Generalized Symmetries in Condensed Matter
• Holographic Mutual Information is Monogamous
• The Holographic Entropy Cone
• Spurious topological entanglement entropy from subsystem symmetries
• Bekenstein-Hawking Entropy as Topological Entanglement Entropy
• The Holographic Entropy Cone for Five Regions
• Spurious Long-range Entanglement and Replica Correlation Length
• Mean string field theory: Landau-Ginzburg theory for 1-form symmetries
• The holographic entropy arrangement
• Holographic Entropy Relations Repackaged
• Symmetry-Protected Topological Interfaces and Entanglement Sequences
• Superbalance of Holographic Entropy Inequalities
• Holographic Entropy Inequalities and Multipartite Entanglement
• Universal lower bound on topological entanglement entropy
• Detecting subsystem symmetry protected topological order via entanglement entropy
• Toy model of boundary states with spurious topological entanglement entropy
• Holographic entropy inequalities and gapped phases of matter
• Properties of the contraction map for holographic entanglement entropy inequalities
• Towards a complete classification of holographic entropy inequalities
• A framework for generalizing toric inequalities for holographic entanglement entropy
• A new characterization of the holographic entropy cone
• Lectures on entanglement in quantum field theory