Quantum Entanglement of Finite-Mean Sachdev-Ye-Kitaev Model

Earlier investigations of the Sachdev-Ye-Kitaev(SYK) model of fermions with all-to-all interactions, have largely focused random coupling strengths drawn from a zero-mean Gaussian distribution. Building on recent developments, we explore a generalized SYK complex fermion model with a non-zero mean in the coupling distribution. This modification is relevant for electrons in the zeroth Landau level of irregular graphene flakes.

Using exact diagonalization for systems of up to N=26, we investigate the many-body density of states (DOS), compressibility, and entropy as a function of temperature T and chemical potential mu. In comparison with the zero mean distribution, we find

(i) the extrapolated entropy at T=0 is reduced;

(ii) the ground-state compressibility increases significantly, with notable changes as a function of mu;

(iii) the entanglement entropy is reduced and confined to each charge sector;

(iv) chaotic behavior is reduced as revealed through level spacing statistics, spectral form factors, and out-of-time-order correlators.