The Sachdev-Ye-Kitaev (SYK) model consists of Q fermions with an all-to-all random two-body hopping [1,2]. Its static state is a non-Fermi liquid with nonzero entropy at vanishing temperature, which is called the Sachdev-Ye (SY) state [3]. Since the SY state has been conjectured to be holographically dual to charged black holes with two-dimensional anti-de Sitter horizons, the SYK model has attracted much attention as a new theoretical tool for studying quantum gravity (see, e.g., Ref. [4]). In this work, we propose a possible route for realizing the SYK model experimentally with use of ultracold gases in optical lattices [5]. We also show how to measure out-of-time-order correlators of the SYK model, which may allow for capturing one of the most crucial characteristics of a black hole, namely maximally chaotic property.
[1] A. Y. Kitaev, “A simple model of quantum holograpy”, KITP string seminar and Entanglement 2015 program (Feb. 12, April 7, and May 27, 2015). http://online.kitp.ucsb.edu/online/entangled15/.
[2] S. Sachdev, Phys. Rev. X 5, 041025 (2015).
[3] S. Sachdev and J. Ye, Phys. Rev. Lett. 70, 3339 (1993).
[4] J. Maldacena and D. Stanford, Phys. Rev. D 94, 106002 (2016).
[5] I. Danshita, M. Hanada, and M. Tezuka, arXiv:1606.02454v2 [cond-mat.quant-gas], to appear in PTEP.