General Relation between Entanglement and Fluctuations in One Dimension

TL;DR

This paper demonstrates that in one-dimensional critical quantum systems, particle number and spin fluctuations scale identically to entanglement entropy, offering a practical way to infer entanglement properties through measurable fluctuations.

Contribution

It establishes a universal relation between fluctuations and entanglement entropy in one-dimensional systems, supported by analytical and numerical evidence, and explores boundary and correction effects.

Findings

Fluctuations scale identically to entanglement entropy in critical systems.

Fluctuations can serve as a practical measure for entanglement scaling.

Boundary effects and subleading corrections influence the scaling behavior.

Abstract

In one dimension very general results from conformal field theory and exact calculations for certain quantum spin systems have established universal scaling properties of the entanglement entropy between two parts of a critical system. Using both analytical and numerical methods, we show that if particle number or spin is conserved, fluctuations in a subsystem obey identical scaling as a function of subsystem size, suggesting that fluctuations are a useful quantity for determining the scaling of entanglement, especially in higher dimensions. We investigate the effects of boundaries and subleading corrections for critical spin and bosonic chains.