Entanglement bounds for single-excitation energy eigenstates of quantum oscillator systems

We provide an analytic method for estimating the entanglement of the non-Gaussian energy eigenstates of disordered harmonic oscillator systems. We invoke the explicit formulas of the eigenstates of the oscillator systems to establish bounds for their \(\epsilon \) $ϵ$ -Rényi entanglement entropy \(\epsilon \in (0,1)\) $ϵ\in (0,1)$ . Our methods result in a logarithmically corrected area law for the entanglement of eigenstates, corresponding to one excitation, of the disordered harmonic oscillator systems.