Kitaev spin models from topological nanowire networks

TL;DR

This paper demonstrates that networks of topological nanowires can emulate exactly solvable Kitaev spin models using Majorana modes, enabling exploration of topological phases and quantum information applications.

Contribution

It establishes a direct connection between topological nanowire networks and Kitaev spin models, including realization of the Yao-Kivelson model and analysis of topological states and their stability.

Findings

Networks can realize Kitaev models with Chern numbers 0, ±1, ±2

Defects correspond to vortex-like quasi-particles

Stability analysis shows resilience against disorder and phase fluctuations

Abstract

We show that networks of topological nanowires can realize the physics of exactly solvable Kitaev spin models with two-body interactions. This connection arises from the description of the low-energy theory of both systems in terms of a tight-binding model of Majorana modes. In Kitaev spin models the Majorana description provides a convenient representation to solve the model, whereas in an array of topological nanowires it arises, because the physical Majorana modes localized at wire ends permit tunnelling between wire ends and across different Josephson junctions. We explicitly show that an array of junctions of three wires -- a setup relevant to topological quantum computing with nanowires -- can realize the Yao-Kivelson model, a variant of Kitaev spin models on a decorated honeycomb lattice. Translating the results from the latter, we show that the network can be constructed to give rise to collective states characterized by Chern numbers \nu = 0, +/-1 and +/-2, and that defects in an array can be associated with vortex-like quasi-particle excitations. Finally, we analyze the stability of the collective states as well as that of the network as a quantum information processor. We show that decoherence inducing instabilities, be them due to disorder or phase fluctuations, can be understood in terms of proliferation of the vortex-like quasi-particles.