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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.17720 |
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Table of Contents:
- Exchangeless braiding of Majorana modes is studied in minimal networks of weakly hybridized Kitaev chains of finite length using a rigorous many-body framework. In particular, for two coupled chains it is shown that exchangeless braiding is achieved by $2π$ rotations of the phase $ϕ$ of the superconducting order parameter of one of the chains. This braiding protocol is verified by the numerical calculation of the non-Abelian Wilczek-Zee phase of the low-energy many-body subspaces ${\cal H}_{0}(ϕ)$ based on the Bertsch-Robledo ground-state overlap formula. In the parameter space spanned by the total chain length, the strength of the weak hybridization connecting the chains, and the on-site potential, we identify two regions with different braiding outcomes, i.e., a projective $σ_{x}$-gate and a projective $σ_{z}$-gate phase. The transition between these phases is a continuous crossover, the location of which is reliably given by a simple four-Majorana mode model. This demonstrates the resilience of the anyonic properties of the Majorana modes against finite-size effects and weak links between Kitaev chains.