Many-body entanglement scaling: Crossover from the ground state to volume laws

Abstract: Entanglement entropies quantify non-locality and operational costs for quantum systems. In ground states of typical condensed matter systems, they obey area and log-area laws. In contrast, subsystem entropies in random and thermal states are extensive, i.e., obey a volume law. For energy eigenstates, one expects a crossover from the groundstate scaling at low energies and small subsystem sizes to the extensive scaling at high energies and large subsystem sizes. We elucidate this crossover. Due to eigenstate thermalization (ETH), the eigenstate entanglement can be related to subsystem entropies in thermodynamic ensembles. For one-dimensional critical systems, the universal crossover function then follows from conformal field theory (CFT). For critical fermions in two dimensions, we obtain a crossover function by employing the 1+1d CFT result for contributions from lines perpendicular to the Fermi surface. Scaling functions for gapped systems additionally depend on a mass parameter. The results are demonstrated numerically for quadratic fermionic systems, finding excellent data collapse to the scaling functions.
Ref: Qiang Miao and Thomas Barthel, arXiv:1905.07760 (2019).