Random-matrix perspective on many-body entanglement with a finite localization length

TL;DR

This paper introduces a random-matrix framework that generalizes Page's law to include finite entanglement localization length, revealing universal behavior across different models and physical systems.

Contribution

It presents a simple, predictive random-matrix model extending Page's law to systems with finite localization length, highlighting universality in many-body entanglement.

Findings

The framework generalizes Page's law for localized systems.

Universal behavior of entanglement localization length across models.

Comparison shows strong universality in entanglement properties.

Abstract

We provide a simple and predictive random-matrix framework that naturally generalizes Page's law for ergodic many-body systems by incorporating a finite entanglement localization length. By comparing a highly structured one-dimensional model to a completely unstructured model and a physical system, we uncover a remarkable degree of universality, suggesting that the effective localization length is a universal combination of model parameters up until it drops down to the microscopic scale.