Logarithmic Corrections to the Entropy of Scalar Field in BTZ Black Hole Space-time

TL;DR

This paper investigates the logarithmic divergence in entanglement entropy for a massive scalar field in (2+1) dimensions, revealing that the universal logarithmic term is unaffected by mass and depends on system properties.

Contribution

It provides a numerical analysis of the logarithmic divergence in entanglement entropy for massive scalar fields in (2+1) dimensions, including mass corrections and their impact.

Findings

Logarithmic divergence term is universal and proportional to conformal anomaly.

Mass corrections do not alter the area law contribution to entanglement entropy.

Universal quantities depend on fundamental properties of the system.

Abstract

The entanglement entropy correlates two quantum sub-systems which are the part of the larger system. A logarithmic divergence term present in the entanglement entropy is universal in nature and directly proportional to the conformal anomaly. We study this logarithmic divergence term of entropy for massive scalar field in $(2+1)$ dimension by applying numerical techniques to entanglement entropy approach. This (2+1) dimensional massive theory can be obtained from (3+1) dimensional massless scalar field via dimensional reduction. We also calculated mass corrections to entanglement entropy for scalar field. Finally, we observe that the area law contribution to the entanglement entropy is not affected by this mass term and the universal quantities depends upon the basic properties of the system.