Bernard Denis, Piroli Lorenzo
Laboratoire de Physique de l'École Normale Supérieure, CNRS, ENS & PSL University, Sorbonne Université, Université de Paris, 75005 Paris, France.
Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany.
Phys Rev E. 2021 Jul;104(1-1):014146. doi: 10.1103/PhysRevE.104.014146.
We study the probability distribution of entanglement in the quantum symmetric simple exclusion process, a model of fermions hopping with random Brownian amplitudes between neighboring sites. We consider a protocol where the system is initialized in a pure product state of M particles, and we focus on the late-time distribution of Rényi-q entropies for a subsystem of size ℓ. By means of a Coulomb gas approach from random matrix theory, we compute analytically the large-deviation function of the entropy in the thermodynamic limit. For q>1, we show that, depending on the value of the ratio ℓ/M, the entropy distribution displays either two or three distinct regimes, ranging from low to high entanglement. These are connected by points where the probability density features singularities in its third derivative, which can be understood in terms of a transition in the corresponding charge density of the Coulomb gas. Our analytic results are supported by numerical Monte Carlo simulations.
我们研究了量子对称简单排斥过程中纠缠的概率分布，这是一个费米子在相邻格点间以随机布朗振幅跳跃的模型。我们考虑一种协议，其中系统初始化为M个粒子的纯积态，并且我们关注大小为ℓ的子系统的Rényi - q熵的晚期分布。通过随机矩阵理论中的库仑气体方法，我们在热力学极限下解析地计算了熵的大偏差函数。对于q > 1，我们表明，根据ℓ/M的比值，熵分布呈现出两种或三种不同的状态，范围从低纠缠到高纠缠。这些状态由概率密度的三阶导数出现奇点的点相连，这可以根据库仑气体相应电荷密度的转变来理解。我们的解析结果得到了数值蒙特卡罗模拟的支持。
