# Condensed Matter Seminars

## "Crossover functions for entanglement entropy in many-body energy eigenstates and universality"

**Thomas Barthel , Duke University**

[Host: Israel Klich ]

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.

References: PRL 127, 040603 (2021); PRA 104, 022414 (2021); arXiv:2010.07265.

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