Topological insulators with arbitrarily tunable entanglement

Abstract

We elucidate how Chern and topological insulators fulfill an area law for the entanglement entropy. By explicit construction of a family of lattice Hamiltonians, we are able to demonstrate that the area law contribution can be tuned to an arbitrarily small value, but is topologically protected from vanishing exactly. We prove this by introducing novel methods to bound entanglement entropies from correlations using perturbation bounds, drawing intuition from ideas of quantum information theory. This rigorous approach is complemented by an intuitive understanding in terms of entanglement edge states. These insights have a number of important consequences: The area law has no universal component, no matter how small, and the entanglement scaling cannot be used as a faithful diagnostic of topological insulators. This holds for all Renyi entropies which uniquely determine the entanglement spectrum which is hence also non-universal. The existence of arbitrarily weakly entangled topological insulators furthermore opens up possibilities of devising correlated topological phases in which the entanglement entropy is small and which are thereby numerically tractable, specifically in tensor network approaches.

9 pages, 3 figures, final version

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Cited by in corpus (6)

• Entanglement Spectrum and Entanglement Hamiltonian of a Chern insulator with open boundaries
• Correlations and entanglement in flat band models with variable Chern numbers
• Diagnosing Topological Edge States via Entanglement Monogamy
• Anatomy of Fermionic Entanglement and Criticality in Kitaev Spin Liquids
• A search for correlation-induced adiabatic paths between distinct topological insulators
• Entanglement studies of interacting fermionic models