Universality in the Entanglement and Localization of Strongly Chaotic Subsystems
The entanglement and localization in eigenstates of bipartite systems with strongly chaotic subsystems are studied as a function of interaction strength. Excellent measures for this purpose are the von-Neumann entropy, Havrda-Charvát-Tsallis entropies, and the inverse participation ratio. All the entropies are shown to follow a remarkably simple exponential form, which describes a universal and rapid transition to nearly maximal entanglement for increasing interaction strength. An unexpectedly exact relationship between the subsystem averaged inverse participation ratio and purity (linear entropy) is derived that infers the transition in the localization as well.