# Universality in volume law entanglement of pure quantum states

## TL;DR

This paper derives a universal analytic formula for entanglement entropy in pure quantum states representing thermal equilibrium, applicable to various states and useful for diagnosing chaos and localization.

## Contribution

It introduces a universal formula for entanglement entropy applicable to a broad class of thermal states, linking quantum correlations with thermodynamics.

## Key findings

- The formula applies to cTPQ states and general energy eigenstates of non-integrable models.
- It can distinguish between integrable and chaotic systems.
- It effectively detects many-body localization.

## Abstract

A pure quantum state can fully describe thermal equilibrium as long as one focuses on local observables. Thermodynamic entropy can also be recovered as the entanglement entropy of small subsystems. When the size of the subsystem increases, however, quantum correlations break the correspondence and cause a correction to this simple volume-law. To elucidate the size dependence of the entanglement entropy is of essential importance in linking quantum physics with thermodynamics, and in addressing recent experiments in ultra-cold atoms. Here we derive an analytic formula of the entanglement entropy for a class of pure states called cTPQ states representing thermal equilibrium. We further find that our formula applies universally to any sufficiently scrambled pure states representing thermal equilibrium, i.e., general energy eigenstates of non-integrable models and states after quantum quenches. Our universal formula can be exploited as a diagnostic of chaotic systems; we can distinguish integrable models from chaotic ones and detect many-body localization with high accuracy.