Density of States of Quantum Spin Systems from Isotropic Entanglement

TL;DR

The paper introduces Isotropic Entanglement, a method to predict eigenvalue distributions of quantum spin systems by interpolating between known approximations, achieving high accuracy beyond traditional moment-based methods.

Contribution

It presents a universal interpolation technique for spectral prediction in quantum spin systems that surpasses traditional moment-matching approaches.

Findings

IE accurately predicts eigenvalue distributions

The method is universal across different local interactions

Outperforms traditional moment-based approximations

Abstract

We propose a method which we call "Isotropic Entanglement" (IE), that predicts the eigenvalue distribution of quantum many body (spin) systems (QMBS) with generic interactions. We interpolate between two known approximations by matching fourth moments. Though, such problems can be QMA-complete, our examples show that IE provides an accurate picture of the spectra well beyond what one expects from the first four moments alone. We further show that the interpolation is universal, i.e., independent of the choice of local terms.