Institut für Theorie der Kondensierten Materie, Karlsruher Institut für Technologie, 76128, Karlsruhe, Germany.
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoe shosse 31, 115409, Moscow, Russia.
Sci Rep. 2017 May 3;7(1):1447. doi: 10.1038/s41598-017-01413-z.
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.
基于马约拉纳量子比特的量子计算机将包含大量零能马约拉纳态。该系统可以被建模为交错“平凡”和“拓扑”区域的伊辛- Kitaev 链的连接网络，零能马约拉纳费米子定域在它们的界面处。描述这种网络的理论的低能部分可以用马约拉纳零模之间的主要阶耦合来表述。我考虑了一个表现出四个马约拉纳零模之间有效耦合的最小模型 - 非均匀伊辛- Kitaev 链，包含两个由“平凡”区域隔开的“拓扑”区域。通过精确求解该模型，我表明对于模型参数的一般值，四个零模被局域在链的四个界面点处。在存在额外的反转对称性的特殊情况下，马约拉纳零模在两个界面点之间“离域”。在这两种情况下，理论的低能部分都可以用局域马约拉纳费米子来表述，但它们之间的一些耦合与它们各自的分离无关：精确解不支持有效低能哈密顿量的“最近邻”形式。
