Witnessing Entanglement in Mixed-Particle Quantum Systems

TL;DR

This paper presents an entanglement witness that detects and quantifies off-diagonal long-range order in mixed fermionic and bosonic systems, revealing how collective entanglement emerges from many-body correlations.

Contribution

It introduces a novel entanglement witness based on particle-hole reduced density matrices for mixed particles, capable of identifying and quantifying ODLRO across different particle types.

Findings

Detects ODLRO independently in fermionic and bosonic sectors

Quantifies the combined entanglement from fermionic and bosonic correlations

Shows transition from localized to shared ODLRO indicating collective entanglement

Abstract

We introduce an entanglement witness that identifies off-diagonal long-range order (ODLRO) -- a distinctive form of entanglement -- in systems containing both fermionic and bosonic particles. By analyzing the particle-hole reduced density matrices of each subsystem, the approach detects ODLRO independently in both fermionic and bosonic sectors and identifies when long-range order develops across the entire mixed-particle system. The witness also quantifies the magnitude of ODLRO within each particle type, revealing how fermionic and bosonic correlations combine to form the total entanglement of the system, including a bosonic condensation of particle-hole pairs driven by many-body correlations rather than particle statistics. Using the Lipkin-Meshkov-Glick spin model, we show how the transition from ODLRO localized to one particle type to ODLRO shared by both particle types captures the onset of collective entanglement in a mixed-particle environment, providing new insight into systems where fermionic and bosonic correlations coexist.