Eigenstate entanglement scaling for critical interacting spin chains
With increasing subsystem size and energy, bipartite entanglement entropies of energy eigenstates cross over from the groundstate scaling to a volume law. In previous work, we pointed out that, when strong or weak eigenstate thermalization (ETH) applies, the entanglement of all or, respectively, almost all eigenstates follow universal scaling functions which are determined by the subsystem entropy of thermal states. This was demonstrated by field-theoretical arguments and by analysis of large systems of non-interacting fermions and bosons. Here, we further substantiate such scaling properties for integrable and non-integrable interacting spin-1/2 chains at criticality using exact diagonalization. In particular, we analyze XXZ and transverse-field Ising models with and without next-nearest-neighbor interactions. We first confirm that the crossover for subsystem entropies in thermal ensembles can be described by a universal scaling function following from conformal field theory. Then, we analyze the validity of ETH for entanglement in these models. Even for the relatively small system sizes that can be simulated, the distributions of eigenstate entanglement entropies are sharply peaked around the subsystem entropies of the corresponding thermal ensembles.