We present numerical studies of fermion and boson models with random all-to-all interactions (the SYK models). The high temperature expansion and exact diagonalization of the N-site fermion model are used to compute the entropy density: our results are consistent with the numerical solution of N = 1 saddle point equations, and the presence of a non-zero entropy density in the limit of vanishing temperature. The exact diagonalization results for the fermion Green’s function also appear to converge well to the N = 1 solution. For the hard-core boson model, the exact diagonalization study indicates spin glass order. Some results on the entanglement entropy and the out-of-time-order correlators are also presented.Physic
