A proposal to extract and enhance four-Majorana interactions in hybrid nanowires.

The Sachdev-Ye-Kitaev (SYK) model is an N-Majorana model with 4-body random all to all interactions. It is exactly solvable in large N-limit and mimics black holes physics, thus providing insights to the theory of quantum gravity. In this work, we simulate smallest unit of the SYK model, i.e., a 4-MZM (quartic) interaction model in a 1D nanowire system. We model a 3-segment Kitaev chain hosting 4 MZMs and add a non-local interaction term to introduce quartic interaction in the MZMs. We tune this system to the SYK criteria by minimizing other (2-body/bilinear) interactions and enhancing the quartic interaction. Extracting and tuning these interacting strengths is done by analyzing energy level spacings between even and odd parity states of a 2-complex-fermion model that resembles low-energy level physics of the interacting Kitaev chain model. We propose that this study can be performed in an experimental setup since eigenspectral characterization of 1D nanowire devices can be done in quantum transport measurements. We further propose that this model could be extended to an N>4 MZM SYK model and present an N=6 model as an example.