paper

Eigenstate entanglement: Crossover from the ground state to volume laws

arXiv:1905.07760 · doi:10.1103/PhysRevLett.127.040603

Abstract

For the typical quantum many-body systems that obey the eigenstate thermalization hypothesis (ETH), we argue that the entanglement entropy of (almost) all energy eigenstates is described by a single crossover function. The ETH implies that the crossover functions can be deduced from subsystem entropies of thermal ensembles and have universal properties. These functions capture the full crossover from the groundstate entanglement regime at low energies and small subsystem size (area or log-area law) to the extensive volume-law regime at high energies or large subsystem size. For critical one-dimensional systems, a universal scaling function follows from conformal field theory (CFT) and can be adapted for nonlinear dispersions. We use it to also deduce the crossover scaling function for Fermi liquids in dimensions. The analytical results are complemented by numerics for large non-interacting systems of fermions in , , and dimensions and have also been confirmed for bosonic systems and non-integrable spin chains. Furthermore, one can deduce the distribution function for eigenstate entanglement.

arXiv comment8 pages, 8 figures, 1 table, including 3 appendices. Improved text, added data and figures. The follow-up papers arXiv:1912.10045 and arXiv:2010.07265 address bosonic and non-integrable systems

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