Two-local modifications of SYK model with quantum chaos
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911477162573824 |
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| author | Hanada, Masanori van Leuven, Sam Oktay, Onur Tezuka, Masaki |
| author_facet | Hanada, Masanori van Leuven, Sam Oktay, Onur Tezuka, Masaki |
| contents | 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., $H=\sum_{p,q}J_{pq}χ_pχ_{p+1}χ_qχ_{q+1}$ instead of the original SYK Hamiltonian $H=\sum_{p,q,r,s}J_{pqrs}χ_pχ_qχ_rχ_{s}$), 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09900 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two-local modifications of SYK model with quantum chaos Hanada, Masanori van Leuven, Sam Oktay, Onur Tezuka, Masaki Quantum Physics Disordered Systems and Neural Networks Strongly Correlated Electrons High Energy Physics - Theory 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., $H=\sum_{p,q}J_{pq}χ_pχ_{p+1}χ_qχ_{q+1}$ instead of the original SYK Hamiltonian $H=\sum_{p,q,r,s}J_{pqrs}χ_pχ_qχ_rχ_{s}$), 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. |
| title | Two-local modifications of SYK model with quantum chaos |
| topic | Quantum Physics Disordered Systems and Neural Networks Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2505.09900 |