Divergence of entanglement entropy in quantum systems: Zero-modes

TL;DR

This paper investigates the divergence of entanglement entropy caused by zero-modes in quantum systems, providing new insights into their behavior and implications for field theory and gravity.

Contribution

It introduces a free particle approximation of the harmonic oscillator to analyze zero-mode entropy divergences in continuous quantum systems and explores their implications.

Findings

Zero-mode divergences are easier to isolate than UV divergences.

Entropy divergence observed in coupled oscillators and hydrogen atom models.

Implications for field theory and IR structure of gravity discussed.

Abstract

To this day, von Neumann definition of entropy remains the most popular measure of quantum entanglement. Much of the literature on entanglement entropy, particularly in the context of field theory, has focused on isolating the UV divergences. Zero-mode divergences of the entanglement entropy are less studied in this context, and apart from being easier to isolate, they offer an interesting insight into the physics of the system. To gain a better understanding of the system in this limit, we develop the free particle approximation of Harmonic oscillator, with which we investigate the properties of entropy divergence in continuous bi-partite quantum systems such as the coupled Harmonic oscillators and the Hydrogen atom. We also show zero-mode divergence of the entropy of environment-induced entanglement in a tri-partite oscillator system. We discuss the implications of our result for field theory and IR structure of gravity.