Dresden 2014 – scientific programme
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TT: Fachverband Tiefe Temperaturen
TT 82: Low-Dimensional Systems: Topological Order (organized by TT)
TT 82.7: Talk
Thursday, April 3, 2014, 11:00–11:15, HSZ 204
Topological insulators with arbitrarily tunable entanglement scaling — •Jan Carl Budich1, Jens Eisert2, and Emil Johansson Bergholtz2 — 1Department of Physics, Stockholm University, SE-106 91 Stockholm, Sweden — 2Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
We elucidate how Chern and topological insulators fulfill an area law for the entanglement entropy. By ex- plicit 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 and complement this approach by an intuitive understanding. These insights have a number of important conse- quences. The non-universality implies that the entanglement scaling cannot be used as a faithful diagnostic of topological insulators. The existence of arbitrarily weakly entangled topological insulators opens up possibili- ties of devising correlated topological phases in which the entanglement entropy is small and which are thereby numerically tractable, specifically in tensor network approaches.