Malpetti Daniele, Roscilde Tommaso
Laboratoire de Physique, CNRS UMR 5672, Ecole Normale Supérieure de Lyon, Université de Lyon, 46 Allée d'Italie, Lyon F-69364, France.
Institut Universitaire de France, 103 boulevard Saint-Michel, 75005 Paris, France.
Phys Rev Lett. 2016 Sep 23;117(13):130401. doi: 10.1103/PhysRevLett.117.130401. Epub 2016 Sep 21.
Nonlocality is a fundamental trait of quantum many-body systems, both at the level of pure states, as well as at the level of mixed states. Because of nonlocality, mixed states of any two subsystems are correlated in a stronger way than what can be accounted for by considering the correlated probabilities of occupying some microstates. In the case of equilibrium mixed states, we explicitly build two-point quantum correlation functions, which capture the specific, superior correlations of quantum systems at finite temperature, and which are directly accessible to experiments when correlating measurable properties. When nonvanishing, these correlation functions rule out a precise form of separability of the equilibrium state. In particular, we show numerically that quantum correlation functions generically exhibit a finite quantum coherence length, dictating the characteristic distance over which degrees of freedom cannot be considered as separable. This coherence length is completely disconnected from the correlation length of the system-as it remains finite even when the correlation length of the system diverges at finite temperature-and it unveils the unique spatial structure of quantum correlations.
非定域性是量子多体系统的一个基本特征，无论是在纯态层面，还是在混合态层面。由于非定域性，任何两个子系统的混合态以一种比通过考虑占据某些微观态的相关概率所能解释的更强的方式相关联。在平衡混合态的情况下，我们明确构建两点量子关联函数，它捕捉了有限温度下量子系统的特定的、优越的相关性，并且在关联可测量性质时可直接用于实验。当这些关联函数不为零时，它们排除了平衡态的一种精确的可分离形式。特别地，我们通过数值计算表明，量子关联函数通常表现出有限的量子相干长度，它决定了自由度不能被视为可分离的特征距离。这个相干长度与系统的关联长度完全无关——即使系统的关联长度在有限温度下发散，它仍然是有限的——并且它揭示了量子关联独特的空间结构。
