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TT: Fachverband Tiefe Temperaturen
TT 3: Correlated Electrons: Low-Dimensional Systems - Models 1
TT 3.13: Vortrag
Montag, 11. März 2013, 12:45–13:00, H9
Characterization of Topological Phase Transitions: A Tensor-Product State Approach — •Siddhardh Chandra1, Frank Pollmann1, and Norbert Schuch2 — 1Max-Planck-Institut für Physik komplexer Systeme, Dresden, Germany — 2RWTH Aachen University, Aachen, Germany
We investigate phase transitions between phases with non-trivial topological order. Topological order is a kind of order that cannot be explained with the traditional approach of Landau's symmetry breaking and local order parameters. However, it can be characterized by other quantities such as the braiding statistics of the excitations in the model. Due to recent advances in numerical techniques, it has become possible to extract these statistics from the ground-state wavefunction of a model. We consider simple string-net models, which are known to have topological order, and analyze the behavior of various quantities as we move from one topological phase to another. The useful formalism of tensor-product states allows us to create a tunable representation which helps us to study the behavior of the entanglement spectrum and modular matrices which characterize the statistics of the anyonic excitations in the two phases. We identify some of the defining components of a topological phase transition as opposed to a symmetry breaking transition and discuss the possible extensions to other models with topological order.