Berlin 2015 – wissenschaftliches Programm

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HL: Fachverband Halbleiterphysik

HL 85: Topological Insulators 2 (MA with HL/TT)

HL 85.11: Vortrag

Donnerstag, 19. März 2015, 17:30–17:45, EB 202

Matrix product operators: Local equivalences and topological order in 2D — •Oliver Buerschaper — Freie Universität Berlin

Projected entangled pair states (PEPS), which naturally generalize matrix product states (MPS) to higher dimensions, describe the low energy properties of local quantum Hamiltonians with an energy gap very well. For this reason they are increasingly used as a valuable tool in both analytical and numerical studies of strongly correlated 2D quantum systems. Some of the most interesting such systems exhibit topological order, i.e. patterns of long-range entanglement which cannot be detected by any local order parameter. At the same time, excitations in these systems typically exhibit fractional statistics and may be used, for instance, as a resource for topological quantum computation.

For both fundamental and practical reasons, it is thus of the utmost importance to understand and classify PEPS in 2D, especially those with topological order. Recently it was found that symmetries defined in terms of certain matrix product operators (MPO) provide a mechanism for the emergence of topological order in PEPS. Furthermore, the kind of topological order was seen to depend on the algebraic properties of the given MPO symmetry. Here we show that many, seemingly distinct MPO symmetries are, in fact, locally equivalent and characterize PEPS with the same kind of topological order. We discuss interesting ramifications for the classification of 2D quantum systems.