[Paper Review] Entanglement in Many-Body Systems

Luigi Amico, Rosario Fazio+2 more|arXiv (Cornell University)|Mar 6, 2007

Advanced Thermodynamics and Statistical Mechanics4 citations

TL;DR

This comprehensive review explores entanglement in many-body quantum systems, analyzing its role in quantum phase transitions, thermodynamic properties, and dynamics across spin, fermion, and boson models. It establishes connections between entanglement measures and observable quantities like criticality and correlation functions, offering experimental detection via entanglement witnesses and highlighting its central role in quantum information and condensed matter physics.

ABSTRACT

The recent interest in aspects common to quantum information and condensed matter has prompted a prosperous activity at the border of these disciplines that were far distant until few years ago. Numerous interesting questions have been addressed so far. Here we review an important part of this field, the properties of the entanglement in many-body systems. We discuss the zero and finite temperature properties of entanglement in interacting spin, fermionic and bosonic model systems. Both bipartite and multipartite entanglement will be considered. At equilibrium we emphasize on how entanglement is connected to the phase diagram of the underlying model. The behavior of entanglement can be related, via certain witnesses, to thermodynamic quantities thus offering interesting possibilities for an experimental test. Out of equilibrium we discuss how to generate and manipulate entangled states by means of many-body Hamiltonians.

Motivation & Objective

• To systematically analyze the role of entanglement in many-body quantum systems across different models and interactions.
• To connect entanglement properties to thermodynamic and critical phenomena, especially at zero and finite temperature.
• To develop and apply entanglement measures—bipartite, multipartite, localizable, and topological—for diverse quantum systems.
• To explore the dynamics of entanglement generation and propagation in open quantum systems and spin chains.
• To provide a theoretical framework for the experimental detection of entanglement using entanglement witnesses and thermodynamic proxies.

Proposed method

• Utilizes bipartite and multipartite entanglement measures, including concurrence, localizable entanglement, and entanglement entropy.
• Applies entanglement witnesses to detect entanglement in mixed states and relate it to measurable thermodynamic quantities.
• Employs quantum information techniques such as density matrix renormalization group (DMRG) and Gaussian state formalism for numerical and analytical treatment.
• Analyzes entanglement entropy scaling in one-dimensional systems, verifying the area law and studying deviations in critical and topological phases.
• Investigates entanglement dynamics via time evolution under many-body Hamiltonians, including non-Markovian and open system models.
• Integrates renormalization group methods with entanglement analysis to study quantum criticality and universal scaling behavior.

Experimental results

Research questions

• RQ1 How does entanglement characterize quantum phase transitions in spin chains and fermionic models?
• RQ2 To what extent can entanglement be detected experimentally using thermodynamic observables and entanglement witnesses?
• RQ3 What is the role of entanglement in topological order and long-range quantum correlations in many-body systems?
• RQ4 How does entanglement propagate in non-equilibrium dynamics of spin and harmonic lattices?
• RQ5 Can multipartite entanglement measures reveal new insights into strongly correlated systems like high-Tc superconductors?

Key findings

• Entanglement entropy in one-dimensional systems follows the area law, with logarithmic corrections at critical points, confirming universal scaling behavior.
• Localizable entanglement exhibits sharp peaks at quantum critical points, signaling enhanced non-local correlations.
• Thermal entanglement witnesses can detect entanglement in mixed states at finite temperature, providing a pathway for experimental validation.
• Pairwise entanglement in spin chains is maximized near quantum phase transitions and correlates strongly with magnetic order parameters.
• In harmonic lattices, entanglement propagation is mediated by collective modes, with boundary oscillators becoming entangled after a finite signal travel time.
• Topological entanglement entropy provides a robust signature of topological order, with a universal contribution of -γ = -ln(2) in certain models.