Optical lattice platform for the Sachdev-Ye-Kitaev model
Chenan Wei, Tigran Sedrakyan
Abstract
The tractability of the Sachdev-Ye-Kitaev (SYK) model at the large $N$ limit makes it ideal to theoretically study its chaotic non-Fermi liquid behavior and holographic duality properties. We show that the complex SYK Hamiltonian emerges from a system of spinless itinerant fermionic atoms in an optical kagome lattice with a strong disorder. We discuss the regimes supporting flat band spectra in a kagome lattice, where the system can be nondispersive. Random interaction between nondispersive fermions is induced due to randomly distributed immobile impurities in the optical lattice, that impede the presence of itinerant fermions at their locations. We show that the proposed setup represents a maximally chaotic system and is a reliable experimental platform to realize the SYK model and study its exotic behavior. We show that the velocity distribution of the released fermions is a sensitive probe of the many-body Wigner-Dyson spectral density of states while the averaged many-body Loschmidt echo scheme can measure two-point out-of-time-ordered correlation functions of the SYK system.