Entropy of entanglement and multifractal exponents for random states

TL;DR

This paper establishes a relationship between the entropy of entanglement in random states and their multifractal properties, providing insights into entanglement near the Anderson transition.

Contribution

It introduces a novel connection between entanglement entropy and multifractal exponents, expanding understanding of entanglement in complex quantum systems.

Findings

First-order entropy depends on participation ratio

Higher-order entropy involves multifractal exponents

Results applicable to Anderson transition phenomena

Abstract

We relate the entropy of entanglement of ensembles of random vectors to their generalized fractal dimensions. Expanding the von Neumann entropy around its maximum we show that the first order only depends on the participation ratio, while higher orders involve other multifractal exponents. These results can be applied to entanglement behavior near the Anderson transition.