Entanglement properties and ground-state statistics of free bosons

TL;DR

This paper provides an analytical framework for calculating entanglement, correlation functions, and statistical properties of free bosons on a lattice, unifying these calculations through a reduced density matrix approach.

Contribution

It introduces a unified method to derive entanglement measures and correlation functions of free bosons using a multinomial form of the reduced density matrix.

Findings

All quantities can be derived from the reduced density matrix

The approach applies to both homogeneous and inhomogeneous systems

Provides explicit formulas for entanglement and correlation functions

Abstract

We calculate analytically the entanglement and R\'enyi entropies, the negativity and the mutual information together with all the density and many-particle correlation functions for free bosons on a lattice in the ground state, for both homogeneous and inhomogeneous systems. We show that all those quantities can be derived from a multinomial form of the reduced density matrix in the configuration space whose diagonal elements dictate the statistics of the particle distribution, while the off-diagonal coherence terms control the quantum fluctuations. We provide by this analysis a unified approach based on a reduced density matrix technique useful to calculate both the entanglement properties and an infinite number of correlation functions.