Majorana fermions in the nonuniform Ising-Kitaev chain: exact solution

Abstract

A quantum computer based on Majorana qubits would contain a large number of zero-energy Majorana states. This system can be modelled as a connected network of the Ising-Kitaev chains alternating the "trivial" and "topological" regions, with the zero-energy Majorana fermions localized at their interfaces. The low-energy sector of the theory describing such a network can be formulated in terms of leading-order couplings between the Majorana zero modes. I consider a minimal model exhibiting effective couplings between four Majorana zero modes - the nonuniform Ising-Kitaev chain, containing two "topological" regions separated by a "trivial" region. Solving the model exactly, I show that for generic values of the model parameters the four zero modes are localized at the four interface points of the chain. In the special case where additional inversion symmetry is present, the Majorana zero modes are "delocalized" between two interface points. In both cases, the low-energy sector of the theory can be formulated in terms of the localized Majorana fermions, but the couplings between some of them are independent of their respective separations: the exact solution does not support the "nearest-neighbor" form of the effective low-energy Hamiltonian.

11 pages, 8 figures

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Cited by in corpus (6)

• Universal two-time correlations, out-of-time-ordered correlators and Leggett-Garg inequality violation by edge Majorana fermion qubits
• Emulating Majorana fermions and their braiding by Ising spin chains
• Detuning the Honeycomb of the α-RuCl3 Kitaev lattice: A case of Cr3+ dopant
• Decoherence and relaxation of topological states in extended quantum Ising models
• Coherent multiple-period states in a resonantly driven qubit
• Nonuniform Parafermion Chains: Low-Energy Physics and Finite-Size Effects