标题： 随机量子场态的Fock空间纠缠 显示英文标题

标题： Entanglement in Fock space of random QFT states

摘要： 纠缠在随机态中已经发展成为量子热化和黑洞物理的一个有用方法。 本文中，我们将“随机酉矩阵框架”细化并扩展到量子场论（QFT），并包括守恒荷。 我们展示，在QFT中，在Fock基底下，典型态、约化子系统和热动力学之间的联系更加清晰。 我们提供了任意粒子子集的典型约化密度矩阵和纠缠熵的通用公式。 为了说明我们的方法，我们将通用框架应用于最简单但非平凡的情况，即二维中的无质量标量场及其推广到N个标量场的情形，包括大N极限。 我们通过将约化动力学与吉布斯系综匹配来找到有效温度，并推导出QFT的状态方程。 偏离完全热化的偏差被证明是1/S的数量级，而不是exp(-S)，这一结果可能对黑洞物理有重要意义。 最后，我们描述了QFT场景中所谓的“Page曲线”作为能量尺度的函数，该能量尺度划分了高能和低能自由度。 显示英文摘要

摘要： Entanglement in random states has turned into a useful approach to quantum thermalization and black hole physics. In this article, we refine and extend the `random unitaries framework' to quantum field theories (QFT), and to include conserved charges. We show that in QFT, the connection between typical states, reduced subsystems and thermal dynamics is more transparent within the Fock basis. We provide generic formulae for the typical reduced density matrices and entanglement entropies of any given subset of particles. To illustrate our methods, we apply the generic framework to the simplest but non trivial cases, a massless scalar field in two dimensions and its generalization to the case of N scalar fields, including the large N limit. We find the effective temperature, by matching the reduced dynamics to a Gibbs ensemble, and derive the equation of state of the QFT. The deviations from perfect thermality are shown to be of order 1/S instead of exp(-S), a result which might be relevant for black hole physics. Finally we describe the analogue of the so-called `Page curve' in the QFT scenario as a function of the energy scale which divides high from low energy degrees of freedom.