基于迹距离的有限温度下的量子相变理论研究

项目名称： 基于迹距离的有限温度下的量子相变理论研究

项目编号： No.11504140

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 胡征达

作者单位： 江南大学

项目金额： 20万元

中文摘要： 量子相变一直是凝聚态物理中的研究热点，而随着量子信息理论的发展，许多非经典量，如纠缠、量子discord以及保真度等，已经被广泛用于研究量子相变。本项目利用迹距离以及基于迹距离的非经典关联来描述有限温度的量子相变，选取典型的腔QED及自旋系统，重点研究有限温度下这些迹距离量对量子相变点的探测，找出在临界区所遵循的标度行为和幂律，进一步讨论温度对量子相变探测的影响等问题。主要研究内容包括：（1）Dicke模型中的原子-腔场热初始关联；（2）一维光纤耦合的腔QED量子网络在热态下的两态迹距离和原子-原子迹距离discord；（3）热自旋系统中的两自旋迹距离discord以及重整化后块自旋中的迹距离discord。迹距离的良好物理特性以及基于迹距离的非经典量的可实验性，极大地方便了对有限温度的量子相变的研究。本研究为进一步从量子信息角度理解量子相变提供理论参考。

中文关键词： 量子信息；迹距离；量子相变；腔QED系统；自旋系统

英文摘要： Quantum phase transition is always a hot issue in condensed matter physics. As the development of quantum information theory, various quantities such as entanglement, quantum discord and fidelity have been used to study quantum phase transition. This project is devoted to investigating quantum phase transition at finite temperature via trace distance and nonclassical correlations based on trace distance. By considering paradigmatic models in cavity QED and spin systems, we focus on the detection of quantum phase transition at finite temperature with these quantities. The scaling behavior and power law associated are found and the effect of temperature is further discussed. The main content includes: (1) thermal initial correlation of atom-cavity in Dicke model; (2) trace distance of thermal states and trace distance discord of atom-atom in one dimensional quantum networks of cavity QED; (3) trace distance discord of two spins in thermal spin systems and that in spin blocks under renormalization. The nice properties of trace distance as well as the feasibility of these nonclassical quantities based on trace distance in experiments actually do a great favor to the study of quantum phase transition at finite temperature. These studies may provide theoretical references for further understanding of quantum phase transition from the perspective of quantum information.

英文关键词： quantum information;trace distance;quantum phase transition;cavity QED system;spin system