Stretched exponential decay of Majorana edge modes in many-body localized Kitaev chains under dissipation

TL;DR

This paper studies how Majorana edge modes in disordered Kitaev chains decay under dissipation, revealing a universal stretched exponential decay with an exponent around 2/3, even in many-body localized phases.

Contribution

It demonstrates that disorder-induced many-body localization can significantly stabilize Majorana modes against symmetry-breaking dissipation, leading to a universal decay behavior.

Findings

Majorana modes decay exponentially in homogeneous systems under dissipation.

Strong disorder and many-body localization slow down decay, leading to stretched exponential behavior.

Universal decay exponent approximately 2/3 for particle loss dynamics.

Abstract

We investigate the resilience of symmetry-protected topological edge states at the boundaries of Kitaev chains in the presence of a bath which explicitly introduces symmetry-breaking terms. Specifically, we focus on single-particle losses and gains, violating the protecting parity symmetry, which could generically occur in realistic scenarios. For homogeneous systems, we show that the Majorana mode decays exponentially fast. By the inclusion of strong disorder, where the closed system enters a many-body localized phase, we find that the Majorana mode can be stabilized substantially. The decay of the Majorana converts into a stretched exponential form for particle losses or gains occuring in the bulk. In particular, for pure loss dynamics we find a universal exponent $\alpha \simeq 2/3$. We show that this holds both in the Anderson and many-body localized regimes. Our results thus provide a first step to stabilize edge states even in the presence of symmetry-breaking environments.