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arXiv · 1704.09017

Frustration-free Hamiltonians supporting Majorana zero edge modes

Sania Jevtic·Ryan Barnett
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Abstract

A one-dimensional fermionic system, such as a superconducting wire, may host Majorana zero-energy edge modes (MZMs) at its edges when it is in the topological phase. MZMs provide a path to realising fault-tolerant quantum computation, and so are the focus of intense experimental and theoretical studies. However, given a Hamiltonian, determining whether MZMs exist is a daunting task as it relies on knowing the spectral properties of the Hamiltonian in the thermodynamic limit. The Kitaev chain is a paradigmatic non-interacting model that supports MZMs and the Hamiltonian can be fully diagonalised. However, for interacting models, the situation is far more complex. Here we consider a different classification of models, namely, ones with frustration-free Hamiltonians. Within this class of models, interacting and non-interacting systems are treated on an equal footing, and we identify exactly which Hamiltonians can realise MZMs.

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Sania Jevtic, Ryan Barnett. 2017-04-28. Frustration-free Hamiltonians supporting Majorana zero edge modes. https://doi.org/10.1088/1367-2630/aa88da

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