Eigenstate entanglement scaling for critical interacting spin chains

TL;DR

This paper investigates how eigenstate entanglement entropy in critical interacting spin chains scales with subsystem size, demonstrating universal behavior consistent with conformal field theory and validating ETH for entanglement.

Contribution

It provides the first numerical evidence that entanglement entropy crossover functions in critical spin chains follow universal scaling laws predicted by conformal field theory.

Findings

Eigenstate entanglement entropies follow universal crossover functions.

Thermal subsystem entropies describe eigenstate entanglement scaling.

Eigenstate thermalization hypothesis holds for entanglement in these models.

Abstract

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 entropies of all or, respectively, almost all eigenstates follow a single crossover function. The crossover functions are determined by the subsystem entropy of thermal states and assume universal scaling forms in quantum-critical regimes. This was demonstrated by field-theoretical arguments and the analysis of large systems of non-interacting fermions and bosons. Here, we 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. Indeed, the crossover of thermal subsystem entropies can be described by a universal scaling function following from conformal field theory. Furthermore, 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.