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

Abstract

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 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.

15 pages, 4 figures, published version

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Cited by in corpus (23)

• Quantum Optimization of Maximum Independent Set using Rydberg Atom Arrays
• Universality of Phase Transition Dynamics: Topological Defects from Symmetry Breaking
• Anyon condensation and its applications
• Space-time renormalization in phase transition dynamics
• Scaling and diabatic effects in quantum annealing with a D-Wave device
• Correlation function diagnostics for type-I fracton phases
• Dynamic scaling at classical phase transitions approached through non-equilibrium quenching
• Kibble-Zurek Mechanism and Finite-Time Scaling
• Realistic scheme for quantum simulation of ${\mathbb{Z}}_2$ lattice gauge theories with dynamical matter in $(2+1)$D
• Quench dynamics and parity blocking in Majorana wires
• Topological Blocking in Quantum Quench Dynamics
• Quantum Quench and Scaling of Entanglement Entropy
• Kibble-Zurek scaling of the irreversible entropy production
• Dynamics and correlations at a quantum phase transition beyond Kibble-Zurek
• Quench Dynamics Across Topological Quantum Phase Transitions
• Universal Early Coarsening of Quenched Bose Gases
• Phase transitions in three-dimensional topological lattice models with surface anyons
• Destruction of string order after a quantum quench
• Quantum Brownian motion in a Landau level
• Topological Phase Transitions Induced by Varying Topology and Boundaries in the Toric Code
• Shortcuts to Analog Preparation of Non-Equilibrium Quantum Lakes
• Kibble-Zurek scaling from linear response theory
• Entanglement Spreading and Oscillation