Entanglement dynamics in the three-dimensional Anderson model

TL;DR

This paper investigates entanglement dynamics in a 3D Anderson model, revealing critical scaling behaviors at the metal-insulator transition that resemble those in many-body localized phases, suggesting a nuanced understanding of localization.

Contribution

It demonstrates that entanglement and number entropy exhibit critical scaling at the Anderson transition, linking non-interacting and many-body localization phenomena.

Findings

Logarithmic growth of entanglement entropy at the transition

Number entropy scales as ln ln t, similar to MBL phases

Critical properties are consistent with other probes

Abstract

We numerically study the entanglement dynamics of free fermions on a cubic lattice with potential disorder following a quantum quench. We focus, in particular, on the metal-insulator transition at a critical disorder strength and compare the results to the putative many-body localization (MBL) transition in interacting one-dimensional systems. We find that at the transition point the entanglement entropy grows logarithmically with time $t$ while the number entropy grows $\sim\ln\ln t$. This is exactly the same scaling recently found in the MBL phase of the Heisenberg chain with random magnetic fields suggesting that the MBL phase might be more akin to an extended critical regime with both localized and delocalized states rather than a fully localized phase. We also show that the experimentally easily accessible number entropy can be used to bound the full entanglement entropy of the Anderson model and that the critical properties at the metal-insulator transition obtained from entanglement measures are consistent with those obtained by other probes.