Entanglement Entropy of A Simple Non-minimal Coupling Model

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.