Rényi entropies are conceptually valuable and experimentally relevant generalizations of the celebrated von Neumann entanglement entropy. After a quantum quench in a clean quantum many-body system they generically display a universal linear growth in time followed by saturation. While a finite subsystem is essentially at local equilibrium when the entanglement saturates, it is genuinely out of equilibrium in the growth phase. In particular, the slope of the growth carries vital information on the nature of the system’s dynamics, and its characterization is a key objective of current research. Here we show that the slope of Rényi entropies can be determined by means of a spacetime duality transformation. In essence, we argue that the slope coincides with the stationary density of entropy of the model obtained by exchanging the roles of space and time. Therefore, very surprisingly, the slope of the entanglement is expressed as an equilibrium quantity. We use this observation to find an explicit exact formula for the slope of Rényi entropies in all integrable models treatable by thermodynamic Bethe ansatz and evolving from integrable initial states. Interestingly, this formula can be understood in terms of a quasiparticle picture only in the von Neumann limit.

中文翻译：

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交互可积模型中 Rényi 熵的增长和准粒子图像的分解

Rényi 熵是著名的冯诺依曼纠缠熵在概念上有价值且与实验相关的概括。在干净的量子多体系统中发生量子猝灭后，它们通常会随着时间的推移呈现出普遍的线性增长，然后是饱和。虽然当纠缠饱和时，有限子系统基本上处于局部平衡状态，但在生长阶段它确实处于失衡状态。特别是，增长的斜率承载了有关系统动力学性质的重要信息，其表征是当前研究的一个关键目标。在这里，我们表明 Rényi 熵的斜率可以通过时空对偶变换来确定。在本质上，我们认为斜率与通过交换空间和时间的角色获得的模型的固定熵密度一致。因此，非常令人惊讶的是，纠缠的斜率被表示为一个平衡量。我们使用这一观察结果为所有可积模型中的 Rényi 熵的斜率找到一个明确的精确公式，这些模型可由热力学 Bethe ansatz 处理并从可积初始状态演变而来。有趣的是，这个公式只能根据冯诺依曼极限的准粒子图像来理解。