Berlin 2015 – scientific programme

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HL: Fachverband Halbleiterphysik

HL 77: Low-dimensional systems: Topological order 1 (TT with HL)

HL 77.1: Talk

Thursday, March 19, 2015, 11:30–11:45, H 3010

Towards a complete characterization of 2d topological order using tensor networks and multipartite entanglement — •Roman Orus — Johannes-Gutenberg Universität, Mainz, Deutschland

Topological order in a 2d quantum matter can be determined by the topological contribution to the entanglement Renyi entropies. However, when close to a quantum phase transition, its calculation becomes cumbersome. In this talk I will show how topological phase transitions in 2d systems can be much better assessed by multipartite entanglement, as measured by the topological geometric entanglement of blocks. Specifically, I will present an efficient tensor network algorithm based on Projected Entangled Pair States (PEPS) to compute this quantity for a torus partitioned into cylinders, and then use this method to find sharp evidence of topological phase transitions in 2d systems with a string-tension perturbation. When compared to tensor network methods for Renyi entropies, this approach produces almost perfect accuracies close to criticality and, on top, is orders of magnitude faster. Moreover, I will show how the method also allows the identification of Minimally Entangled States (MES), thus providing a very efficient and accurate way of extracting the full topological information of a 2d quantum lattice model from the multipartite entanglement structure of its ground states.