Partially Ordered Sachdev-Ye-Kitaev (SYK) Models

The Sachdev-Ye-Kitaev (SYK) model describes all-to-all four-body interactions between spins. In studies so far, these couplings have been chosen randomly from a distribution with zero mean. Motivated by recent claims that SYK models may be relevant to describe the behavior of electrons in Landau levels in graphene flakes, we expand the investigation of SYK models with couplings chosen from distributions with a non-zero mean. For SYK models with complex fermions as well as for majorana fermions, we have obtained the density of states, statistics of level spacings, spectral form factor, and some information about out of time order correlator (OTOCs), operator growth, and entanglement entropy in order to understand their quantum chaotic properties. We observe distinct differences between the zero mean and finite mean cases. To obtain further insights into our results, we have performed a mean field analysis on this model.