Disconnected entanglement entropy as a marker of edge modes in a periodically driven Kitaev chain

TL;DR

This paper demonstrates that disconnected entanglement entropy (DEE) can serve as an effective marker for detecting Floquet Majorana edge modes in a periodically driven Kitaev chain, showing robustness against disorder and noise.

Contribution

It introduces DEE as a quantized indicator of Floquet Majorana edge modes in driven Kitaev chains, including anomalous modes, and explores its behavior under disorder and in a kicked Ising model.

Findings

DEE is integer-quantized and equals the number of Majorana edge modes.

Majorana edge modes are robust against weak disorder and noise.

DEE can detect anomalous edge modes without topological significance.

Abstract

We study the disconnected entanglement entropy (DEE) of a Kitaev chain in which the chemical potential is periodically modulated with $\delta$-function pulses within the framework of Floquet theory. For this driving protocol, the DEE of a sufficiently large system with open boundary conditions turns out to be integer-quantized, with the integer being equal to the number of Majorana edge modes localized at each edge of the chain generated by the periodic driving, thereby establishing the DEE as a marker for detecting Floquet Majorana edge modes. Analysing the DEE, we further show that these Majorana edge modes are robust against weak spatial disorder and temporal noise. Interestingly, we find that the DEE may, in some cases, also detect the anomalous edge modes which can be generated by periodic driving of the nearest-neighbor hopping, even though such modes have no topological significance and not robust against spatial disorder. We also probe the behaviour of the DEE for a kicked Ising chain in the presence of an integrability breaking interaction which has been experimentally realized.