Multiscale entanglement clusters at the many-body localization phase transition

TL;DR

This paper investigates the structure of entanglement clusters during the many-body localization transition, revealing a transition from strong to weak entanglement and identifying fractal-like multiscale entangled states at criticality.

Contribution

It introduces a numerical analysis of entanglement cluster formation across the transition, highlighting multiscale entanglement structures and their implications for theoretical models.

Findings

Critical states exhibit fractal or multiscale entanglement structures.

Cluster size distribution follows a power-law at the transition.

Localized phase shows exponential decay in cluster sizes.

Abstract

We study numerically the formation of entanglement clusters across the many-body localization phase transition. We observe a crossover from strong many-body entanglement in the ergodic phase to weak local correlations in the localized phase, with contiguous clusters throughout the phase diagram. Critical states close to the transition have a structure compatible with fractal or multiscale-entangled states, characterized by entanglement at multiple levels: small strongly entangled clusters are weakly entangled together to form larger clusters. The critical point therefore features subthermal entanglement and a power-law distributed cluster size, while the localized phase presents an exponentially decreasing cluster distribution. These results are consistent with some of the recently proposed phenomenological renormalization-group schemes characterizing the many-body localized critical point, and may serve to constrain other such schemes.