标题： 精确的有限约化密度矩阵和Calogero模型的冯·诺依曼熵 显示英文标题

标题： Exact finite reduced density matrix and von Neumann entropy for the Calogero model

摘要： 连续量子变量系统的信息内容通常使用一些已知的近似方法进行研究。 这些近似是为了获得光谱、本征函数或约化密度矩阵，这些对于计算量化信息的类似熵量是必不可少的。 即使在光谱和本征函数精确已知的稀疏情况下，必须以近似方式获得表征该问题的约化密度矩阵的光谱，即{\em 即}。 在本工作中，我们解析地得到了N粒子Calogero模型基态的约化密度矩阵的有限表示，适用于相互作用参数的一组离散值。 作为结果，精确的纠缠光谱和冯·诺依曼熵被推导出来。 显示英文摘要

摘要： The information content of continuous quantum variables systems is usually studied using a number of well known approximation methods. The approximations are made to obtain the spectrum, eigenfunctions or the reduced density matrices that are essential to calculate the entropy-like quantities that quantify the information. Even in the sparse cases where the spectrum and eigenfunctions are exactly known the entanglement spectrum, {\em i.e.} the spectrum of the reduced density matrices that characterize the problem, must be obtained in an approximate fashion. In this work, we obtain analytically a finite representation of the reduced density matrices of the fundamental state of the N-particle Calogero model for a discrete set of values of the interaction parameter. As a consequence, the exact entanglement spectrum and von Neumann entropy is worked out.