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

TL;DR

This paper numerically investigates fermion and boson models with infinite-range random interactions, confirming theoretical predictions and revealing spin glass order in bosons, with insights into entropy and quantum chaos.

Contribution

It provides numerical validation of analytical solutions for SYK models and explores entanglement and chaos properties in these systems.

Findings

Entropy density remains non-zero at zero temperature.

Fermion Green's function converges to large-N solution.

Boson model exhibits spin glass order.

Abstract

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 $N=\infty$ 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 $N=\infty$ 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.