The effect of gluon condensate on the entanglement entropy in a holographic model

Abstract: In this study, we examine the impact of the gluon condensate on holographic entanglement entropy within an Einstein-Dilaton model at both zero and finite temperatures. A critical length exists for the difference in entanglement entropy between connected and disconnected surfaces in this model, which is typically interpreted as an indicator of phase transition. As the gluon condensate increases, the critical length decreases, suggesting that confinement strengthens at zero temperature. Additionally, the entropic C-function abruptly drops to zero at the critical length, indicating the absence of entangled states. At finite temperatures, the results show that the effect of the gluon condensate on the critical length is qualitatively similar to that at zero temperature. We observe that the entropic C-function increases as a function of $L$ at finite temperature, though it exhibits competitive behaviors when the gluon condensate is large.