| 题名 | 低维量子自旋系统的杂质效应研究 |
| 作者 | 黄旭初 |
| 学位类别 | 博士 |
| 答辩日期 | 2015-05-20 |
| 授予单位 | 中国科学院大学 |
| 授予地点 | 北京 |
| 导师 | 杨志华 |
| 关键词 | 自旋系统 Ising 模型 严格解 杂质效应 |
| 学位专业 | 微电子学与固体电子学 |
| 中文摘要 | 低维量子自旋系统作为低维磁体理论载体，成为凝聚态物理一个主要的研究课题。与复杂三维系统相比较，低维磁体因强的量子涨落会产生一系列奇特量子效应如量子反常霍尔效应、高温超导电性、庞磁阻效应等。其中作为能够进行近似求解的磁性材料模型之一，Ising模型可以用于分析讨论很多凝聚态自旋系统，尤其是在其基础上发展的各种变形可以从理论上和实验上研究量子相变、量子纠缠、临界现象等。随着实验科学技术的发展，量子自旋系统因掺杂而产生了许多奇特的物理性质，杂质也成为了影响量子涨落的一个重要指标，这引发了实验学者对含杂质磁性材料的研究兴趣和理论学者们对杂质模型的探索热潮。然而杂质系统研究领域仍存在着诸多尚未攻克或尚未明确的难题。例如由于量子涨落，杂质将破坏系统的局域关联，影响系统激发谱的能隙，但系统的无序变化与产生能隙的物理本质并不清楚。目前在理论和实验上仍无法对杂质引起的有序-无序行为给出清晰的物理图像，其中一个重要的原因是由于杂质破坏了系统的对称性使得杂质系统的求解比较困难，制约了杂质对体系基态、激发态、热力学性质、量子相变、量子纠缠等影响机理研究。因此在低维含杂质自旋模型严格求解基础上探索杂质效应对于新型磁性材料的研制和开发具有重要意义。本文在严格求解含单/多个S=1/2或S=1杂质的Ising模型基础上，研究了体系杂质的不同构型、浓度、各向异性、局域磁场等因素对体系影响。揭示了杂质对系统基态的量子调控行为，量子自旋链中的量子纠缠和量子相变内在关联，杂质引起的磁性有序-无序行为，以及在低温区域杂质的热力学奇异行为。具体研究成果如下：（1）含单个S=1/2杂质系统的长程序和短程序均受到杂质-体系耦合强度影响；自旋-自旋关联函数不可解析点的位置与不含杂质系统相比具有明显的偏移，证明杂质可充当横向磁场作用；在弱磁场情况下杂质的近邻纠缠随外磁场和杂质耦合作用的变化会出现一个小的奇异峰，并且存在一个纠缠阈值，显示杂质对量子纠缠具有调控作用。（2）对于含多个S=1/2杂质的自旋模型，形变能隙是杂质的局域磁场作用、杂质-体系耦合相互作用的单调函数，并且受外磁场的调节。通过计算杂质的局域磁矩发现杂质-体系耦合强度以及杂质局域磁场的作用导致了杂质附件产生局域效应，但这种杂质局域效应确使得系统有序-无序相变点偏离了无杂质系统的量子临界点。杂质系统的热力学行为与外磁场作用紧密相关，在强磁场作用下更容易看到杂质的热力学双峰现象， 其主要原因是杂质和磁场协同的量子效应导致。此外，当杂质的浓度大于3%时系统的杂质效应就变得非常明显。（3）为对比S=1/2 杂质模型，本文研究了含S=1 杂质的横场Ising 模型。与S=1/2 杂质系统相比，含S=1 杂质的系统由于自由度的增加会使该系统展现出更为丰富的量子相变行为。通过对比热系数的研究发现，在零温极限下这两类系统的比热系数均趋向同一常数，说明他们属于同一普适类。但杂质自旋为1 的体系在低温区域出现了一个小的奇异峰，并且小的奇异峰仅仅出现在含S=1 杂质的系统，通过研究杂质系统的激发行为发现该奇异峰来自于杂质空穴激发，且比热峰出现的位置在T ~ imp，从本质上来说空 穴激发是S=1/2 杂质和S=1 杂质系统差异的主要因素。（4）根据含S=1 多杂质自旋链的结构特点，对于热力学极限条件下系统的配分函数可以通过有限尺寸下系统配分函数的迭代获得。本文详细分析了的杂质激发行为，计算了在增加杂质浓度的过程中系统基态的量子相变行为。通过研究杂质系统的热力学行为，发现比热奇异峰与外磁场的变化紧密相关，杂质自旋粒子之间的耦合作用对λ-型比热峰具有明显的调节作用，意味着杂质自旋粒子和主链自旋粒子之间的相互竞争是调控系统有序-无序相变的主要因素。本文提出的严格求解多杂质自旋模型方法可以求解较为复杂的含杂质自旋模型(包括近邻、次近邻杂质耦合作用自旋链、XY 自旋链等)，从而更加准确的认识量子磁性杂质引起的复杂物理现象，并为实现对量子态和量子临界性的调控提供明确的理论基础。用扩展的数值迭代方法在热力学极限情况下严格求解杂质的热力学效应，这对研究杂质在低温区域所展现的奇异性以及杂质与量子相变之间的内在关系具有重要意义。总之，本文的研究在含杂质的量子自旋系统的解析、数值方法上有所突破，为认识杂质在磁性材料中的作用提供明确的理论依据，为其他新型功能材料设计、模拟、性能计算开拓新思路。 |
| 英文摘要 | Low-dimensional quantum spin systems have been the subject of considerable investigation in condensed matter physics because of the novel phenomena originating from their low dimensionality and strong quantum fluctuations. The low dimensional spin systems are more easy to get the exact solution compared with the complicated three-dimensional systems(e.g., Quantum Anomalous Hall Effect, High Temperature Superconductivity, Colossal Magnetoresistance, etc.), which attracts many theoretical physicists. Ising model is one of the important magnetic material models, because a number of condensed matter systems can be modelled accurately by Ising model. Many of the intriguing features observed in the statics or dynamics of quantum phase transitions are mostly limited today to either the theoretical investigations in such quantum Ising model or to the experimental results which can be checked and compared for such model. On the other hand, the Ising model is sensitive to disorder in the case of low-dimension, which makes it particularly useful for combined theoretical and experimental studies of disorder in magnets. In recent years, with the development of experimental technology, many novel physics properties have been found in the spin systems because of doping, the impurity has been an important scale for the quantum fluctuation. These novel physics properties cause many experimenters to study magnetic materials with impurity, and many theorists to study the impurity model. However, there exist many unresolved or unclear problem, such as Kondo effect, entanglement related impurity, exact solution, etc. One of the important cases is the order-disorder phenomenon induced by impurity. Owing to the quantum fluctuation, impurity can induce the disorder behavior and cause a small alternation of the intrachain exchange coupling in spin chain, which leads to the opening of a spin gap. It has been proved experimentally that impurity disrupts the local antiferromagnetic correlations, and the spin gap is related to the addition of spin degrees of freedom. However, a complete description of the order-disorder phenomenon related to impurity is still absent. One of the reasons is the limit of method to resolve these corresponding models. It is difficult to exactly solve the impurity problem because impurity breaks the symmetry of system. Especially, there still absents a systematic method to exactly resolve the spin model with high spin impurity or multi-impurity. In this paper, based on the Jordan-Wigner transformation we get a normal method to exactly resolve the spin model with S=1/2 impurity by introducing a proper wave function. We begin with the quantum Ising model with one impurity, and expand the method to the quantum Ising model with may impurities. Considering the different impurity configuration, condense, anisotropy and local magnetic field, we study the impurity effects in ground sate, and the relation between the quantum entanglement and quantum phase transition. We introduce the deformation energy in ground state to analyze the impurity effects for different impurity configuration. We consider the magnetic order-disorder behavior induced by impurity, and the thermal singular behavior in low temperature. In the Ising model with one impurity, we find a small shift exist in the short range order and long range order at the point of with the changes of the coupling between impurity and the nearest host site, and the nonanalytic point changes from to . For the entanglement of impurity, there exists a thresh hold value, which agrees with the XY model with impurity. However, the weak magnetic field can lead to a small anomaly(peak), and the local magnetic field and impurity coupling can control the behavior of anomaly. For the Ising model with many impurities, the result indicates that the deformation energy in the ground state can scale the order-disorder phase transition. The local magnetic field, coupling strength between impurity |
| 公开日期 | 2015-06-15 |
| 内容类型 | 学位论文 |
| 源URL | [http://ir.xjipc.cas.cn/handle/365002/4232]  |
| 专题 | 新疆理化技术研究所_材料物理与化学研究室 |
| 作者单位 | 中国科学院新疆理化技术研究所 |
| 推荐引用方式 GB/T 7714 | 黄旭初. 低维量子自旋系统的杂质效应研究[D]. 北京. 中国科学院大学. 2015. |
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