Spectral correlations and scrambling dynamics in Sachdev-Ye-Kitaev type models

Note: Due to unexpected trouble, we have made the decision to postpone the seminar scheduled for February 21 to May 30. Sorry for the trouble.

Abstract:
The Sachdev-Ye-Kitaev (SYK) model, proposed in 2015, is a quantum mechanical model of N Majorana or complex fermions with all-to-all random four-body interactions. The model has attracted significant attention over the years due to its features such as the existence of the large-N solution with maximally chaotic behavior at low temperatures and holographic correspondence to low-dimensional gravity.
The sparse version of the SYK model reproduces essential features of the original model for reduced numbers of disorder parameters. We recently proposed [1] a further simplification, where we set the nonzero couplings to be +1 or -1 rather than sampling from a continuous distribution such as Gaussian. This binary-coupling model exhibits strong correlations in the spectrum, as observed in the spectral form factor, more efficiently in terms of the number of nonzero terms than in the Gaussian distribution case. We also discuss the scrambling dynamics with the binary-coupling sparse SYK model, comparing the model with the original model as well as the SYK model with random two-body terms [2], where the localization of the many-body eigenstates in the Fock space has been quantitatively studied [3,4].