Two-local modifications of SYK model with quantum chaos

• URL: http://arxiv.org/abs/2505.09900v1
• Date: Thu, 15 May 2025 02:09:00 GMT
• Title: Two-local modifications of SYK model with quantum chaos
• Authors: Masanori Hanada, Sam van Leuven, Onur Oktay, Masaki Tezuka,
• Abstract summary: The Sachdev--Ye--Kitaev (SYK) model may provide us with a good starting point for the experimental study of quantum chaos.<n>We introduce modifications of spin-SYK and SYK models that have similar structures to the SU($d$) model.<n>These models may be a good starting point for the quantum simulation of the original SYK model.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Sachdev--Ye--Kitaev (SYK) model may provide us with a good starting point for the experimental study of quantum chaos and holography in the laboratory. Still, the four-local interaction of fermions makes quantum simulation challenging, and it would be good to search for simpler models that keep the essence. In this paper, we argue that the four-local interaction may not be important by introducing a few models that have two-local interactions. The first model is a generalization of the spin-SYK model, which is obtained by replacing the spin variables with SU($d$) generators. Simulations of this class of models might be straightforward on qudit-based quantum devices. We study the case of $d=3, 4, 5, 6$ numerically and observe quantum chaos already for two-local interactions in a wide energy range. We also introduce modifications of spin-SYK and SYK models that have similar structures to the SU($d$) model (e.g., $H=\sum_{p,q}J_{pq}\chi_p\chi_{p+1}\chi_q\chi_{q+1}$ instead of the original SYK Hamiltonian $H=\sum_{p,q,r,s}J_{pqrs}\chi_p\chi_q\chi_r\chi_{s}$), which shows strongly chaotic features although the interaction is essentially two-local. These models may be a good starting point for the quantum simulation of the original SYK model.

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