1211.0294 (Anushya Chandran et al.)

Kibble-Zurek Scaling and String-Net Coarsening in Topologically Ordered
Systems    [PDF]

Anushya Chandran, F. J. Burnell, Vedika Khemani, S. L. Sondhi

We consider the non-equilibrium dynamics of topologically ordered systems driven across a continuous phase transition into proximate phases with no, or reduced, topological order. This dynamics exhibits scaling in the spirit of Kibble and Zurek but now {\it without} the presence of symmetry breaking and a local order parameter. The late stages of the process are seen to exhibit a slow, coarsening dynamics for the string-net that underlies the physics of the topological phase, a potentially interesting signature of topological order. We also note a time dependent amplification of the energy splitting between topologically degenerate states on closed manifolds. We illustrate these phenomena in the context of particular phase transitions out of the abelian Z_2 topologically ordered phase of the toric code/Z_2 gauge theory, and the non-abelian SU(2)$_k$ ordered phases of the relevant Levin-Wen models.

View original: http://arxiv.org/abs/1211.0294