Excited state entanglement in one dimensional quantum critical systems: Extensivity and the role of microscopic details

We study entanglement via the subsystem purity relative to bipartitions of arbitrary excited states in (1+1)-dimensional conformal field theory, equivalent to the scaling limit of one dimensional quantum critical systems. We compute the exact subpurity as a function of the relative subsystem size for numerous excited states in the Ising and three-state Potts models. We find that it decays exponentially when the system and the subsystem sizes are comparable until a saturation limit is reached near half-partitioning, signaling that excited states are maximally entangled. The exponential behavior translates into extensivity for the second R\'enyi entropy. Since the coefficient of this linear law depends only on the excitation energy, this result shows an interesting, new relationship between energy and quantum information and elucidates the role of microscopic details.