Entanglement and the Born-Oppenheimer approximation in an exactly solvable quantum many-body system

TL;DR

This paper analyzes entanglement in an exactly solvable quantum many-body system, exploring how it depends on particle interactions, masses, and the validity of the Born-Oppenheimer approximation from a quantum information perspective.

Contribution

It provides a detailed study of entanglement behavior in a solvable model, linking it to the Born-Oppenheimer approximation and particle mass differences.

Findings

Entanglement vanishes when subsystems have very different masses.

Maximum entanglement occurs for subsystems of similar mass.

The validity of the Born-Oppenheimer approximation can be understood through entanglement analysis.

Abstract

We investigate the correlations between different bipartitions of an exactly solvable one-dimensional many-body Moshinsky model consisting of Nn "nuclei" and Ne "electrons". We study the dependence of entanglement on the inter-particle interaction strength, on the number of particles, and on the particle masses. Consistent with kinematic intuition, the entanglement between two subsystems vanishes when the subsystems have very different masses, while it attains its maximal value for subsystems of comparable mass. We show how this entanglement feature can be inferred by means of the Born-Oppenheimer Ansatz, whose validity and breakdown can be understood from a quantum information point of view.