Entanglement Entropy of Mixed State in Thermal CFT$_2$

Abstract: Using the subtraction approach, we give the bipartite mixed state entanglement entropy in thermal $\text{CFT}_2$. With these entanglement entropies, we examine a proposed phase transition of entanglement wedge cross section derived from the perspective of bulk investigation in the literature. We clarify the proposed phase transition is an illusion caused by confusion between different configurations. In the thermofield double state, we show a horizon-crossing feature in two-sided entanglement configuration.