Probing Majorana Modes via Local Spin Dynamics

TL;DR

This paper explores how Majorana modes can be detected through local spin dynamics in a quantum spin chain near a critical point, revealing strong zero modes and long coherence times, with potential realization in ion-trap quantum simulators.

Contribution

It demonstrates the emergence of Majorana modes in a Kitaev-Heisenberg spin chain and proposes a method to observe them via two-time spin correlations, connecting spin dynamics to topological Majorana physics.

Findings

Identification of strong zero modes via two-time correlations.

Derivation of a perturbative mapping to Kitaev's fermionic model.

Proposal for realizing Majorana modes in ion-trap quantum simulators.

Abstract

We investigate Majorana modes in a quantum spin chain with bond-dependent exchange interactions by studying its dynamics. Specifically, we consider two-time correlations for the Kitaev-Heisenberg (KH) Hamiltonian close to the so-called Kitaev critical point. Here, the model coincides with a phase boundary of two uncoupled instances of Kitaev's model for p-wave superconductors, together supporting a degenerate ground state characterized by multiple Majorana modes. In this regime, the real-time dynamics of local spins reveal a set of strong zero modes, corresponding to a set of protruding frequencies in the two-time correlation function. We derive perturbative interactions that map the KH spin chain onto the topological regime of Kitaev's fermionic model, thus opening up a bulk gap whilst retaining almost degenerate modes in the mesoscopic regime, i.e., for finite system sizes. This showcases the emergence of Majorana modes in a chain of effective dimers. Here, the binding energy within each unit cell competes with the inter-dimer coupling to generate a finite size energy gap, in analogy with local energy terms in the transverse-field Ising model. These modes give rise to long coherence times of local spins located at the system edges. By breaking the local symmetry in each dimer, one can also observe a second class of Majorana modes in terms of a beating frequency in the two-time correlations function of the edge spin. Furthermore, we develop a scenario for realizing these model predictions in ion-trap quantum simulators with collective addressing of the ions.