Kibble-Zurek scaling and string-net coarsening in topologically ordered systems

Area of Science:

• Condensed matter physics
• Quantum field theory
• Topological phases of matter

Background:

• Topological order describes phases of matter with long-range entanglement and no local order parameter.
• Continuous phase transitions typically involve symmetry breaking and local order parameters (Kibble-Zurek mechanism).

Purpose of the Study:

• Investigate non-equilibrium dynamics of topologically ordered systems driven across continuous phase transitions.
• Explore scaling behaviors and identify potential signatures of topological order in the absence of symmetry breaking.

Main Methods:

• Analysis of non-equilibrium dynamics in topologically ordered systems.
• Study of phase transitions into phases with reduced or no topological order.
• Examination of string-net coarsening dynamics.

Main Results:

• Observed scaling dynamics analogous to the Kibble-Zurek mechanism, but without symmetry breaking.
• Identified slow coarsening dynamics of the underlying string-net as a key feature.
• Illustrated phenomena in Abelian Z2 topological phases (toric code) and non-Abelian SU(2)k phases (Levin-Wen models).

Conclusions:

• Non-equilibrium dynamics in topological systems exhibit unique scaling properties distinct from symmetry-breaking transitions.
• String-net coarsening dynamics serve as a potential experimental signature for topological order.
• The findings provide insights into the nature of topological order and its behavior during phase transitions.