Entanglement and localization of wavefunctions
O. Giraud, J. Martin, B. Georgeot
TL;DR
This paper reviews how the entanglement of wavefunctions relates to their localization properties, connecting entropy measures to localization metrics and demonstrating relevance to physical systems through simulations.
Contribution
It establishes a simple relation between entanglement entropy and localization measures, extending to multifractal properties, with numerical validation.
Findings
Linear entropy relates to inverse participation ratio
Higher-order entanglement entropies encode multifractal exponents
Numerical results match physical system wavefunction entanglement
Abstract
We review recent works that relate entanglement of random vectors to their localization properties. In particular, the linear entropy is related by a simple expression to the inverse participation ratio, while next orders of the entropy of entanglement contain information about e.g. the multifractal exponents. Numerical simulations show that these results can account for the entanglement present in wavefunctions of physical systems.
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