Exact results on the quench dynamics of the entanglement entropy in the toric code

TL;DR

This paper provides exact analytical results on the time evolution of entanglement entropy in the 2D toric code model after a quantum quench, revealing persistent area law behavior and effects of disorder and integrability breaking.

Contribution

It offers the first exact calculations of entanglement dynamics in the 2D toric code and analyzes the impact of disorder and magnetic fields on entanglement scaling.

Findings

Area law persists at all times after quench

Disorder leads to saturation of entanglement entropy independent of disorder strength

Topological entropy remains zero throughout the evolution

Abstract

We study quantum quenches in the two-dimensional Kitaev toric code model and compute exactly the time-dependent entanglement entropy of the non-equilibrium wave-function evolving from a paramagnetic initial state with the toric code Hamiltonian. We find that the area law survives at all times. Adding disorder to the toric code couplings makes the entanglement entropy per unit boundary length saturate to disorder-independent values at long times and in the thermodynamic limit. There are order-one corrections to the area law from the corners in the subsystem boundary but the topological entropy remains zero at all times. We argue that breaking the integrability with a small magnetic field could change the area law to a volume scaling as expected of thermalized states but is not sufficient for forming topological entanglement due to the presence of an excess energy and a finite density of defects.