# Eigenstate entanglement: Crossover from the ground state to volume laws

## TL;DR

This paper investigates how eigenstate entanglement entropy transitions from area-law to volume-law in quantum many-body systems, revealing universal crossover functions derived from thermal ensemble properties and supported by numerical simulations.

## Contribution

It introduces a universal crossover function for eigenstate entanglement entropy applicable across various quantum systems, connecting ground state and volume-law regimes.

## Key findings

- Universal crossover function describes entanglement entropy transition
- Analytical results derived from conformal field theory and thermal ensembles
- Numerical validation across fermionic, bosonic, and spin systems

## 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.