Isotropic Entanglement

TL;DR

Isotropic Entanglement is a novel method inspired by Free Probability and Random Matrix Theory that accurately predicts eigenvalue distributions in quantum many-body systems by interpolating between classical and isotropic extremes.

Contribution

The paper introduces the Isotropic Entanglement method, proving key theorems and demonstrating its universality and accuracy beyond traditional moment-based predictions.

Findings

Proves Matching Three Moments and Slider Theorems.

Shows the interpolation's universality, independent of local terms.

Demonstrates high accuracy of IE in quantum systems.

Abstract

The method of "Isotropic Entanglement" (IE), inspired by Free Probability Theory and Random Matrix Theory, predicts the eigenvalue distribution of quantum many-body (spin) systems with generic interactions. At the heart is a "Slider", which interpolates between two extrema by matching fourth moments. The first extreme treats the non-commuting terms classically and the second treats them isotropically. Isotropic means that the eigenvectors are in generic positions. We prove Matching Three Moments and Slider Theorems and further prove that the interpolation is universal, i.e., independent of the choice of local terms. Our examples show that IE provides an accurate picture well beyond what one expects from the first four moments alone.