Monte Carlo Studies of entanglement and mutual information in interacting quantum many-body systems

本提案的目标是基于最近开发的无偏大尺度量子蒙特卡罗模拟方案，系统地探索二维和三维相互作用量子多体系统在有限温度下的纠缠特性和互信息。对纠缠熵中面积定律的普遍次导修正将在具有常规和拓扑有序相以及近量子相变和量子相变的磁模型中进行分析。这些校正项的普遍性及其与自发对称性破缺、边和角贡献的关系将被评估。这些研究所需的量子蒙特卡罗模拟算法将通过扩展集成方法得到增强。

The goal of this proposal is to provide a systematic exploration of the entanglement properties and mutual information at finite temperature in interacting quantum many-body systems in two and three dimensions based on recently developed, unbiased large scale quantum Monte Carlo simulation schemes. Universal sub-leading corrections to the area law in the entanglement entropy will be analyzed for magnetic models with conventional and topologically ordered phases as well as near and at quantum phase transitions. The universality of such correction terms and their relation to spontaneous symmetry breaking, edge and corner contributions will be assessed. The quantum Monte Carlo simulation algorithms required for these investigations will be augmented by extended ensemble methods.