Numerical study of fermion and boson models with infinite-range random interactions

Abstract

We present numerical studies of fermion and boson models with random all-to-all interactions (the Sachdev-Ye-Kitaev 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 $N=\ensuremath{\infty}$ saddle-point equations, and the presence of a nonzero 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 $N=\ensuremath{\infty}$ 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.