分形晶格上自旋系统量子纠缠与量子相变的研究

项目名称： 分形晶格上自旋系统量子纠缠与量子相变的研究

项目编号： No.11275112

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 孔祥木

作者单位： 曲阜师范大学

项目金额： 80万元

中文摘要： 固体自旋系统具有丰富的纠缠特性而且便于集成，是实现量子信息过程的重要体系之一。几十年来，由于精确求解数学上的困难，对于自旋系统上量子纠缠问题的研究大都集中在小尺度体系上。本项目计划利用统计物理中的重整化群方法研究多体（大尺度）固体自旋系统特别是分形晶格上自旋系统的量子纠缠、量子关联和量子相变等问题。通过计算一维自旋链和分形晶格上相距较远自旋间的量子纠缠和量子关联，研究系统各向异性参数、温度、以及外磁场对量子纠缠和量子关联的影响，研究量子纠缠和量子关联在量子相变点附近的变化特点以及随系统尺度的变化规律。重点探究分形晶格结构对量子纠缠和关联的影响，探究量子纠缠、量子关联与量子相变之间的关系。这些研究对于探寻量子纠缠的控制方法，理解量子相变的本质，以及拓展统计物理方法的应用等都具有重要意义。

中文关键词： 量子纠缠；量子相变；自旋系统；分形；重整化群

英文摘要： Solid spin system, which displays rich entanglement properties and is easy to be integrated, is one of important systems to realize the quantum information processing. In the past few decades, due to the mathematical difficulty in exact solution, previous studies to the entanglement on spin systems have mostly focussed on the small size systems. In this project we plan to study the quantum entanglement, quantum correlation and quantum phase transition of many-body (large size) spin systems especially on the fractal lattices by using the renormalization group method. By calculating the entanglement and quantum correlation between two distant spins on the one-dimensional chains and fractal lattices, the influence of anisotropic parameter, temperature and magnetic field on the entanglement and quantum correlation will be investigated.The behavior of the entanglement and quantum correlation in the vicinity of the quantum phase transition point will be studied. The change of entanglement and quantum correlation with the size of the system will be exposited. We will emphasize on the study of the effect of the system fractal structure on the entanglement or quantum correlation, and the relation between the entanglement or quantum correlation and quantum phase transition. These studies are of great significance to explo

英文关键词： quantum entanglemen；quantum phase transition；spin system；fractal；renormalization group