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Abstract |
We consider the entanglement entropies of energy eigenstates in quantum many-body systems. For the
typical models that allow for a field-theoretical description of the long-range physics, we find that the
entanglement entropy of (almost) all eigenstates is described by a single crossover function. The eigenstate
thermalization hypothesis (ETH) implies that such crossover functions can be deduced from subsystem
entropies of thermal ensembles and that they assume universal scaling forms in quantum-critical regimes.
They describe the full crossover from the groundstate entanglement scaling for low energies and small
subsystem size (area or log-area law) to the extensive volume-law regime for high energies or large
subsystem size. For critical 1d systems, the scaling function follows from conformal field theory (CFT). We
use it to also deduce the scaling function for Fermi liquids in d>1 dimensions. These analytical results are
complemented by numerics for large non-interacting systems of fermions in d=1,2,3 and the harmonic lattice
model (free scalar field theory) in d=1,2. Lastly, we demonstrate ETH for entanglement entropies and the
validity of the scaling arguments in integrable and non-integrable interacting spin chains.
[1] « Eigenstate entanglement: Crossover from the ground state to volume laws”, Phys. Rev. Lett. 127, 040603
(2021)
[2] « Scaling functions for eigenstate entanglement crossovers in harmonic lattices », Phys. Rev. A 104,
022414 (2021)
[3] « Eigenstate entanglement scaling for critical interacting spin chains”, Quantum 6, 642 (2022) |
