# Structure of chaotic eigenstates and their entanglement entropy

## TL;DR

This paper reveals a universal correction to entanglement entropy in chaotic many-body systems, proportional to the square root of heat capacity, linking quantum entanglement to thermodynamic properties.

## Contribution

It generalizes previous findings by showing the correction is universal and relates to thermodynamic quantities, using a refined chaotic eigenstate model.

## Key findings

- Universal correction to entanglement entropy proportional to sqrt of heat capacity.
- Correction depends on thermodynamic properties, not system-specific details.
- Analysis confirms the correction's generality across chaotic systems.

## Abstract

We consider a chaotic many-body system (i.e., one that satisfies the eigenstate thermalization hypothesis) that is split into two subsystems, with an interaction along their mutual boundary, and study the entanglement properties of an energy eigenstate with nonzero energy density. When the two subsystems have nearly equal volumes, we find a universal correction to the entanglement entropy that is proportional to the square root of the system's heat capacity (or a sum of capacities, if there are conserved quantities in addition to energy). This phenomenon was first noted by Vidmar and Rigol in a specific system; our analysis shows that it is generic, and expresses it in terms of thermodynamic properties of the system. Our conclusions are based on a refined version of a model of a chaotic eigenstate originally due to Deutsch, and analyzed more recently by Lu and Grover.