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Eigenstate Entanglement: Crossover from the Ground State to Volume Laws.
1Department of Physics, Duke University, Durham, North Carolina 27708, USA.
Physical Review Letters
|August 6, 2021
Summary
Quantum many-body systems obeying the eigenstate thermalization hypothesis (ETH) show entanglement entropy described by a universal crossover function. This function bridges ground-state entanglement and volume-law regimes across various systems.
Area of Science:
- Quantum Physics
- Condensed Matter Theory
- Statistical Mechanics
Background:
- The Eigenstate Thermalization Hypothesis (ETH) describes thermalization in isolated quantum systems.
- Entanglement entropy in quantum many-body systems exhibits distinct scaling laws (area, volume).
Purpose of the Study:
- To propose a universal crossover function describing entanglement entropy in ETH-obeying systems.
- To connect this function to thermal ensemble properties and universal scaling laws.
Main Methods:
- Derivation of entanglement entropy crossover functions from ETH and thermal ensemble properties.
- Adaptation of conformal field theory scaling functions for critical 1D systems and Fermi liquids.
- Numerical simulations for noninteracting fermions in d≤3 dimensions.
Main Results:
- A single crossover function universally describes entanglement entropy for most energy eigenstates in ETH systems.
- This function captures the transition from area/log-area laws to volume laws with increasing energy or subsystem size.
- Universal scaling functions are derived for critical 1D systems and extended to Fermi liquids.
Conclusions:
- The proposed crossover function provides a unified framework for understanding entanglement entropy in diverse quantum many-body systems.
- ETH provides a powerful tool to deduce universal properties of entanglement entropy.
- The findings are validated across noninteracting fermions, bosonic systems, and spin chains.
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