Eigenstate correlations around many-body localization transition

Understand

We explore correlations of eigenstates around the many-body localization (MBL) transition in their dependence on the energy difference (frequency) $\omega$ and disorder $W$.

• In addition to the genuine many-body problem, XXZ spin chain in random field, we consider localization on random regular graphs (RRG) that serves as a toy model of the MBL transition.
• Both models show a very similar behavior.
• On the localized side of the transition, the eigenstate correlation function $\beta(\omega)$ shows a power-law enhancement of correlations with lowering $\omega$; the corresponding exponent depends on $W$.