基于Jarzynski等式的Rényi熵的非平衡协议
Out-of-equilibrium protocol for Rényi entropies via the Jarzynski equality
摘要：
近年来，诸如冯·诺依曼熵和雷尼熵等纠缠度量为研究量子多体系统的特性提供了一个独特的机会。然而，从分析、实验或数值模拟中提取纠缠特性可能是一项艰巨的任务。在这里，通过结合复制技巧和Jarzynski等式，我们设计了一个新的有效的平衡协议，用于测量平衡Rényi熵。关键思想是在复制品的几何体中执行淬火。Rényi熵作为淬火过程中所作功的指数平均值获得。我们说明了经典的蒙特卡罗模拟的方法的应用，虽然它可能是有用的，在不同的情况下，如在量子蒙特卡罗，或在冷原子系统的实验。该方法在准静态状态下是最有效的，即，对于慢淬火，其中它允许在协议的单个实现中获得Rényi熵。作为一个基准，我们目前的结果在伊辛普适性类$+$尺寸，这是在完美的协议与著名的共形场论（CFT）的预测。
英文摘要：
In recent years entanglement measures, such as the von Neumann and the Rényi entropies, provided a unique opportunity to access elusive feature of quantum many-body systems. However, extracting entanglement properties analytically, experimentally, or in numerical simulations can be a formidable task. Here, by combining the replica trick and the Jarzynski equality we devise a new effective out-of-equilibrium protocol for measuring the equilibrium Rényi entropies. The key idea is to perform a quench in the geometry of the replicas. The Rényi entropies are obtained as the exponential average of the work performed during the quench. We illustrate an application of the method in classical Monte Carlo simulations, although it could be useful in different contexts, such as in Quantum Monte Carlo, or experimentally in cold-atom systems. The method is most effective in the quasi-static regime, i.e., for a slow quench, where it allows to obtain the Rényi entropies in a single realization of the protocol. As a benchmark, we present results for the Rényi entropies in the Ising universality class in $1$$+$$1$ dimensions, which are found in perfect agreement with the well-known Conformal Field Theory (CFT) predictions.
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