Kitaev spin models from topological nanowire networks

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 ν= 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.

15 pages, 9 figures

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Cited by in corpus (16)

• A Short Introduction to Topological Quantum Computation
• Emergent Supersymmetry from Strongly Interacting Majorana Zero Modes
• Roadmap to Majorana surface codes
• Materials design of Kitaev spin liquids beyond the Jackeli-Khaliullin mechanism
• Phase Diagram of the Interacting Majorana Chain Model
• Majorana nanowires for topological quantum computation
• Strongly interacting Majorana fermions
• Majorana bound states in semiconducting nanostructures
• Perturbed vortex lattices and the stability of nucleated topological phases
• Topological Blocking in Quantum Quench Dynamics
• The fate and heir of Majorana zero modes in a quantum wire array
• Protocol Discovery for the Quantum Control of Majoranas by Differentiable Programming and Natural Evolution Strategies
• Subdiffusive dynamics and critical quantum correlations in a disorder-free localized Kitaev honeycomb model out of equilibrium
• Finite temperature geometric properties of the Kitaev honeycomb model
• On critical properties of Berry curvature in Kitaev honeycomb model
• Digital Quantum Simulation of the Kitaev Quantum Spin Liquid