Dresden 2014 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 82: Low-Dimensional Systems: Topological Order (organized by TT)

TT 82.9: Talk

Thursday, April 3, 2014, 12:00–12:15, HSZ 204

Excitation statistics distinguish topologically ordered phases — •Siddhardh Morampudi¹, Curt von Keyserlingk², and Frank Pollmann¹ — ¹Affiliation: Max-Planck-Institut für Physik komplexer Systeme, Dresden, Germany — ²Affiliation: Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, United Kingdom

We investigate the characterization of topologically ordered phases and phase transitions between them. Topological order is a kind of order which cannot be characterized by the traditional approach of Landau's symmetry breaking theory and local order parameters. It is known to arise in diverse systems ranging from the well known fractional quantum hall systems to highly frustrated systems like the Heisenberg antiferromagnet on the Kagome lattice. The lack of local order parameters makes it difficult to uniquely identify a topologically ordered phase and to investigate phase transitions between them.

We consider two topologically ordered phases and use exact diagonalization to look at behaviour of various quantities as we move between them. We find that the usual methods of identifying a topologically ordered phase fail to uniquely distinguish these two phases. We then extract the braiding statistics of the excitations in the phases and use it as a non-local order parameter to distinguish the two phases, finding a first-order transition between them. Finally, we discuss how the approach could easily be generalized to other topologically ordered systems.