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.
Highlights
In this Rapid Communication we present a generalization of Page’s law [1]—central to the statistical description of entanglement in completely ergodic many-body systems—so that it incorporates a finite entanglement length scale, designed to represent an effective localization length in a many-body localized system [2,3,4,5,6]
We proposed a random-matrix framework for many-body quantum systems that captures the effect of finitely ranged entanglement, subsumed into a universal effective entanglement localization length
Just as Page’s law can be utilized as a benchmark to detect deviations from ergodic behavior, the models presented here can serve as a useful benchmark to test concrete hypotheses about disordered many-body systems
Summary
Random-matrix perspective on many-body entanglement with a finite localization length. Marcin Szyniszewski 1,2 and Henning Schomerus 1 1Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom 2Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom (Received 26 October 2019; accepted 25 June 2020; published 8 July 2020). 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
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