Quantifying Unitary Flow Efficiency and Entanglement for Many-Body Localization

TL;DR

This paper investigates the geometry of the Wegner Wilson Flow in many-body localization, focusing on efficiency and entanglement growth, and introduces new bounds and proofs related to entanglement measures and bulk unitary dynamics.

Contribution

It provides a novel connection between boundary entanglement bounds, the Fubini-Study metric, and the information fluctuation complexity in many-body localization.

Findings

Derived upper bounds on boundary entanglement entropy.

Connected entanglement measures to the Fubini-Study metric.

Provided a new, universal proof of the small incremental entangling theorem.

Abstract

We probe the bulk geometry of the Wegner Wilson Flow (WWF) in the context of many-body localization, by addressing efficiency and bulk entanglement growth measures through approximating upper bounds on the boundary entanglement entropy. We connect these upper bounds to the Fubini-Study metric and clarify how a central quantity, the information fluctuation complexity, distinguishes bulk unitary rotation from entanglement production. We also give a short new proof of the small incremental entangling theorem in the absence of ancillas, achieving a dimension-independent, universal factor of $c= 2$.