# Quenched coupling, entangled equilibria, and correlated composite operators: a tale of two O(N) models

## TL;DR

This paper studies the entanglement and thermalization properties of two coupled O(N) models after a quench, revealing insights into entangled states, composite operator correlations, and potential holographic duals.

## Contribution

It introduces a macroscopic entangled state via quenching quadratic couplings in O(N) models and analyzes its properties, connecting free field results to strongly coupled systems.

## Key findings

- Late-time correlation functions mimic strongly coupled systems.
- Partial trace density operator does not commute with Hamiltonian.
- Generalized thermal behavior emerges at late times.

## Abstract

A macroscopic version of Einstein-Podolsky-Rosen entanglement is obtained by quenching a quadratic coupling between two O(N) vector models. A quench of the mixed vacuum produces an excited entangled state, reminiscent of purified thermal equilibrium, whose properties can be studied analytically in the free limit of the individual field theories. The decoupling of different wavelength modes in free field theory prevents true thermalisation but a more subtle difference is that the density operator obtained by a partial trace does not commute with the post-quench Hamiltonian. Generalized thermal behaviour is obtained at late times, in the limit of weak initial mixing or a smooth but rapid quench. More surprisingly, late-time correlation functions of composite operators in the post-quench free field theory share interesting properties with correlators in strongly coupled systems. We propose a holographic interpretation of our result.