Entanglement Entropy of A Simple Non-minimal Coupling Model

TL;DR

This paper calculates the entanglement entropy in a non-minimal Einstein-scalar theory using two methods, confirming the minimal surface restriction and deriving a consistent entropy formula, while extending geometric techniques.

Contribution

It introduces a dual approach to compute entanglement entropy in non-minimal coupling models and generalizes geometric methods to Riemann tensors.

Findings

Entanglement surface is a minimal surface in the model.

Derived entanglement entropy formula matches across methods.

Extended geometric approach to Riemann tensor calculations.

Abstract

We evaluate the entanglement entropy of a non-minimal coupling Einstein-scalar theory with two approaches in classical Euclidean gravity. By analysing the equation of motion, we find that the entangled surface is restricted to be a minimal surface. The entanglement entropy formula is derived directly from the approach of regularized conical singularity. On the other hand, by expressing Ricci scalar of the conical spacetime, we obtain the same result. In addition, we generalize the reduced geometric approach to Riemann tensor and its derivations.