Robustness of the flux-free sector of the Kitaev honeycomb against environment

TL;DR

This paper investigates how Majorana zero modes in the Kitaev honeycomb model respond to environmental decoherence, revealing a quantum Zeno effect and conditions for their robustness in open quantum systems.

Contribution

It provides a detailed analysis of the stability of Majorana zero modes under environmental coupling using a Lindblad master equation approach.

Findings

Steady state tends to be maximally mixed under decoherence.

Quantum Zeno effect observed in density matrix, entropy, and fidelity.

Robustness of MZMs depends on specific parameter regimes, especially in the superconducting Kitaev chain.

Abstract

The Kitaev honeycomb model (KHM) consists of spin-$1/2$ particles on a honeycomb lattice with direction-dependent Ising-like interactions. It can alternatively be described in terms of non-interacting Majorana fermions, can be solved exactly, and has a quantum spin-liquid ground state. Open boundaries then host Majorana zero modes (MZMs) that are robust against some types of disorder. We analyze the fate of the MZMs when they couple to an environment via a Lindblad master equation. By computing the time evolution of the density matrix, we find that when decoherence occurs, the steady state is mostly the maximally mixed state. Among the few exceptions is a parameter regime that realizes the superconducting Kitaev chain model with periodic boundary conditions. We consistently observe a quantum Zeno effect in the density matrix as well as in the entropy and fidelity, while it is not found in the energy gap of some gapped spin liquids. We thus present a comprehensive overview over MZMs coupled to a spin bath that is relevant to proposals to detect MZMs of Kitaev layers on surfaces using scanning tunneling microscopy (STM).