阿贝尔算术Chern-Simons理论中的纠缠熵
Entanglement entropies in the abelian arithmetic Chern-Simons theory
AI总结：
本文在算术Chern-Simons理论中引入纠缠熵概念，针对有限规范群为素数阶循环群的情形，给出了冯·诺依曼纠缠熵的公式。
摘要：
量子力学系统中的纠缠熵概念是一个重要的量，它度量物理态在复合系统中的纠缠程度。在数学上，它度量态向量不能分解为两个希尔伯特空间张量积中元素的程度。本文中，我们寻求其算术对应物：具有有限规范群$G$的算术Chern-Simons理论自然地关联两个量子希尔伯特空间乘积内的一个态向量，并且当$G$是素数阶循环群时，我们给出了该态向量的冯·诺依曼纠缠熵公式。
英文摘要：
The notion of {\em entanglement entropy} in quantum mechanical systems is an important quantity, which measures how much a physical state is entangled in a composite system. Mathematically, it measures how much the state vector is not decomposable as elements in the tensor product of two Hilbert spaces. In this paper, we seek its arithmetic avatar: the theory of arithmetic Chern-Simons theory with finite gauge group $G$ naturally associates a state vector inside the product of two quantum Hilbert spaces and we provide a formula for the {\em von Neumann entanglement entropy} of such state vector when $G$ is a cyclic group of prime order.
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