一种新的乘积熵
A new product entropy
浏览论文内容
中文总结 AI 辅助
本文提出一种新的乘积熵，建立其与SVD纠缠熵的对偶，并解析推导了共形场论中的表达式，通过临界伊辛链数值验证，应用于量子淬火动力学。
中文摘要 AI 辅助
我们提出了一种新的乘积熵，定义为由两个密度矩阵构造的归一化乘积算子的Rényi（或von Neumann）熵。我们建立了一个对偶性，表明两个纯态的子系统的SVD纠缠熵恰好等价于互补子系统的乘积熵。这一联系既提供了基于子系统态乘积的谱多样性的清晰物理解释，也提供了一条绕过约化转移矩阵的计算高效途径。对于低激发本征态，我们推导了二维共形场论中基态与初级激发之间的子系统乘积熵的解析表达式，并针对临界伊辛链进行了明确验证。在量子淬火动力学中，准粒子图像给出了标度极限下的时间演化：在全局淬火后，子系统乘积熵表现出热化和复兴的独特序列，而在局域算子淬火下，它发展出特征平台，其恒定值由插入的算子决定。在临界伊辛链上进行的大量数值计算以极好的精度证实了解析预测。
英文摘要
We propose a new product entropy, defined as the Rényi (or von Neumann) entropy of a normalized product operator constructed from two density matrices. We establish a duality showing that the SVD entanglement entropy of a subsystem for two pure states is exactly equivalent to the product entropy of the complementary subsystem. This connection provides both a transparent physical interpretation in terms of the spectral diversity of the subsystem state product and a computationally efficient route that bypasses the reduced transition matrix. For low-lying eigenstates, we derive analytical expressions for the subsystem product entropy between the ground state and primary excitations in two-dimensional conformal field theories, explicitly verified against the critical Ising chain. In quantum quench dynamics, the quasiparticle picture yields time evolution in the scaling limit: following a global quench, the subsystem product entropy exhibits distinct sequences of thermalization and revivals, whereas under a local operator quench, it develops characteristic plateaus whose constant values are determined by the inserted operator. Extensive numerical calculations on the critical Ising chain confirm the analytical predictions with excellent accuracy.
