Macroscopic Entanglement and Phase Transitions

Abstract

This paper summarises the results of our research on macroscopic entanglement in spin systems and free Bosonic gases. We explain how entanglement can be observed using entanglement witnesses which are themselves constructed within the framework of thermodynamics and thus macroscopic observables. These thermodynamical entanglement witnesses result in bounds on macroscopic parameters of the system, such as the temperature, the energy or the susceptibility, below which entanglement must be present. The derived bounds indicate a relationship between the occurrence of entanglement and the establishment of order, possibly resulting in phase transition phenomena. We give a short overview over the concepts developed in condensed matter physics to capture the characteristics of phase transitions in particular in terms of order and correlation functions. Finally we want to ask and speculate whether entanglement could be a generalised order concept by itself, relevant in (quantum induced) phase transitions such as BEC, and that taking this view may help us to understand the underlying process of high-T superconductivity.

9 pages, 7 figures (color), Submitted to special OSID issue, Proceedings of the 38th Symposium on Mathematical Physics - Quantum Entanglement & Geometry, Torun (Poland), June 2006

References in corpus (5)

• Natural Thermal and Magnetic Entanglement in 1D Heisenberg Model
• Quantum orders in an exact soluble model
• Crucial Role of Quantum Entanglement in Bulk Properties of Solids
• High Temperature Macroscopic Entanglement
• Detecting entanglement with a thermometer

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• Creation of entangled universes avoids the big bang singularity
• Information-theoretic measures of superconductivity in a two-dimensional doped Mott insulator
• Thermal Fluctuations Enhance Order-from-Disorder of Quantum Correlations in Quenched Disordered Spin Models
• How much of one-way computation is just thermodynamics?
• Macroscopic Observables Detecting Genuine Multipartite Entanglement and Partial Inseparability in Many-Body Systems
• Finite-Temperature Scaling of Magnetic Susceptibility and Geometric Phase in the XY Spin Chain
• Increasing complexity with quantum physics