Eigenstate entanglement: Crossover from the ground state to volume laws

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 $d>1$ dimensions. The analytical results are complemented by numerics for large non-interacting systems of fermions in $d=1$, $2$, and $3$ dimensions and have also been confirmed for bosonic systems and non-integrable spin chains. Furthermore, one can deduce the distribution function for eigenstate entanglement.

8 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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• Probing entanglement across the energy spectrum of a hard-core Bose-Hubbard lattice
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• Eigenstate capacity and Page curve in fermionic Gaussian states
• Average entanglement entropy of midspectrum eigenstates of quantum-chaotic interacting Hamiltonians
• Holographic reconstruction of black hole spacetime: machine learning and entanglement entropy
• Exponential shortcut to measurement-induced entanglement phase transitions
• Entanglement Entropy of ($2+1$)-Dimensional SU(2) Lattice Gauge Theory on Plaquette Chains
• Eigenstate entanglement scaling for critical interacting spin chains
• Tight-binding billiards
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• Subsystem entropy in 2d CFT and KdV ETH
• Scaling functions for eigenstate entanglement crossovers in harmonic lattices
• Entanglement Properties of SU(2) Gauge Theory
• Entanglement transition through Hilbert-space localization
• Subsystem eigenstate thermalization hypothesis for translation invariant systems
• Quantum ergodicity and scrambling in quantum annealers
• Power-law banded random matrix ensemble as a model for quantum many-body Hamiltonians
• Entanglement of bosonic systems under monitored evolution
• No eigenstate of the critical transverse-field Ising chain satisfies the area law
• Energy Spectra of Compressed Quantum States
• Trade-off between diagonal and off-diagonal elements in the eigenstate thermalization hypothesis
• Volume-law entanglement fragmentation of quasiparticles