Entanglement entropy scaling laws from fluctuations of non-conserved quantities

TL;DR

This paper proposes a scalable experimental method using reduced fluctuations of local observables to infer entanglement entropy scaling laws in many-body quantum systems, bridging theory and experiment.

Contribution

It introduces a practical protocol to extract entanglement scaling laws from fluctuations, extending previous work to more general systems without conserved quantities.

Findings

Reduced fluctuations scale similarly to entanglement entropy in spin chains.

The method is demonstrated via Density Matrix Renormalization Group calculations.

The approach offers a feasible way to study entanglement experimentally.

Abstract

Entanglement patterns reveal essential information on many-body states and provide a way to classify quantum phases of matter. However, experimental studies of many-body entanglement remain scarce due to their unscalable nature. The present work aims to mitigate this theoretical and experimental divide by introducing reduced fluctuations of observables, consisting of a sum of on-site operators, as a scalable experimental probe of the entanglement entropy. Specifically, we illustrate by Density Matrix Renormalization Group calculations in spin chains that the reduced fluctuations exhibit the same size scaling properties as the entanglement entropy. Generalizing previous observations restricted to special systems with conserved quantities, our work introduces experimentally feasible protocol to extract entanglement scaling laws.