Local response of topological order to an external perturbation

TL;DR

This paper investigates how the Rényi entropies of the toric code respond to perturbations, revealing a unique splitting behavior detectable on small subsystems, which could be experimentally observed.

Contribution

It demonstrates a novel entanglement entropy splitting phenomenon in topological phases, linked to flat entanglement spectra and applicable across various quantum models.

Findings

Rényi entropies of different indices show opposite derivative signs.

The splitting can be detected on small subsystems regardless of correlation length.

The phenomenon is common to phases with certain group theoretic structures.

Abstract

We study the behavior of the R\'enyi entropies for the toric code subject to a variety of different perturbations, by means of 2D density matrix renormalization group and analytical methods. We find that R\'enyi entropies of different index {\alpha} display derivatives with opposite sign, as opposed to typical symmetry breaking states, and can be detected on a very small subsystem regardless of the correlation length. This phenomenon is due to the presence in the phase of a point with flat entanglement spectrum, zero correlation length, and area law for the entanglement entropy. We argue that this kind of splitting is common to all the phases with a certain group theoretic structure, including quantum double models, cluster states, and other quantum spin liquids. The fact that the size of the subsystem does not need to scale with the correlation length makes it possible for this effect to be accessed experimentally.