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 ground-state 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 and can be adapted for nonlinear dispersions. We use it to also deduce the crossover scaling function for Fermi liquids in d > 1 dimensions. Here, the analytical results are complemented by numerics for large noninteracting systems of fermions in d ≤ 3 dimensions and have also been confirmed for bosonic systems and nonintegrable spin chains.
- Authors:
-
- Duke Univ., Durham, NC (United States)
- Publication Date:
- Research Org.:
- Duke Univ., Durham, NC (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1853292
- Alternate Identifier(s):
- OSTI ID: 2280953
- Grant/Contract Number:
- SC0019449
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Volume: 127; Journal Issue: 4; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics; Eigenstate thermalization; Entanglement entropy; Entropy; Quantum entanglement; Scaling laws of complex systems; Conformal field theory; Lattice models in condensed matter
Citation Formats
Miao, Qiang, and Barthel, Thomas. Eigenstate Entanglement: Crossover from the Ground State to Volume Laws. United States: N. p., 2021.
Web. doi:10.1103/physrevlett.127.040603.
Miao, Qiang, & Barthel, Thomas. Eigenstate Entanglement: Crossover from the Ground State to Volume Laws. United States. https://doi.org/10.1103/physrevlett.127.040603
Miao, Qiang, and Barthel, Thomas. Wed .
"Eigenstate Entanglement: Crossover from the Ground State to Volume Laws". United States. https://doi.org/10.1103/physrevlett.127.040603. https://www.osti.gov/servlets/purl/1853292.
@article{osti_1853292,
title = {Eigenstate Entanglement: Crossover from the Ground State to Volume Laws},
author = {Miao, Qiang and Barthel, Thomas},
abstractNote = {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 ground-state 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 and can be adapted for nonlinear dispersions. We use it to also deduce the crossover scaling function for Fermi liquids in d > 1 dimensions. Here, the analytical results are complemented by numerics for large noninteracting systems of fermions in d ≤ 3 dimensions and have also been confirmed for bosonic systems and nonintegrable spin chains.},
doi = {10.1103/physrevlett.127.040603},
journal = {Physical Review Letters},
number = 4,
volume = 127,
place = {United States},
year = {Wed Jul 21 00:00:00 EDT 2021},
month = {Wed Jul 21 00:00:00 EDT 2021}
}
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