Entanglement entropy for a particle coupled with its surrounding

TL;DR

This paper studies how a particle's entanglement with its surrounding lattice increases with stronger confinement and interaction, using a path integral approach in a bipartite lattice model.

Contribution

It introduces a bipartite lattice model with Hooke's law interaction and applies the path integral method to analyze entanglement in the ground state.

Findings

Increasing confining potential increases spatial separation and entanglement.

Hooke's law interaction correlates with higher entanglement.

Path integral approach effectively computes the density matrix.

Abstract

We investigate the entanglement for a model of a particle moving in the lattice (many-body system). The interaction between the particle and the lattice is modelled using Hooke's law. The Feynman path integral approach is applied to compute the density matrix of the system. The complexity of the problem is reduced by considering two-body system (bipartite system). The spatial entanglement of ground state is studied using the linear entropy. We find that increasing the confining potential implies a large spatial separation between the two particles. Thus the interaction between the particles increases according to Hooke's law. This results in the increase in the spatial entanglement.