本文選題：近藤效應　切入點：拓撲量子系統(tǒng)　出處：《南京大學》2017年博士論文　論文類型：學位論文

【摘要】：自上個世紀六十年代以來,近藤效應及其相關(guān)的物理問題一直是凝聚態(tài)理論中一個重要的研究熱點。相關(guān)早期研究不僅促進了重整化群理論方法的建立,而且推動并發(fā)展了基于數(shù)值重整化群的一系列數(shù)值計算方法。另一方面,近年來由于在量子輸運、拓撲量子計算等方向的潛在應用價值,拓撲量子態(tài)物質(zhì)逐漸發(fā)展成為凝聚態(tài)物理中最重要的研究課題之一。多種拓撲材料包括拓撲絕緣體、拓撲半金屬等均已經(jīng)在實驗上實現(xiàn)。一個理論上有趣且具有實際意義的問題是,在新穎的拓撲量子相中,傳統(tǒng)的近藤效應會產(chǎn)生什么新的物理?近藤共振、近藤溫度等是否會和傳統(tǒng)金屬中的近藤效應有所區(qū)別?近藤單態(tài)的形成是否有可能誘導出新的拓撲量子態(tài)?一旦結(jié)合上拓撲量子系統(tǒng),傳統(tǒng)的近藤問題將會產(chǎn)生一系列與之相關(guān)的新的有趣問題。本文主要目的就是初步探索并回答這些問題。第一章我將為本文即將研究的兩個課題做出簡要概述。對于近藤問題,我從研究歷史的角度出發(fā),闡述了它的發(fā)展過程,回顧了歷史中重要的進展。對于拓撲量子系統(tǒng),我主要試圖回答拓撲是什么以及怎么去刻畫拓撲態(tài)。第二章是關(guān)于近藤效應的微擾處理。首先我針對非磁性雜質(zhì)問題討論了T矩陣解法。接著利用T矩陣方法處理了無相互作用的安德森模型。對于安德森模型和s-d交換模型,我們采用近藤提出的微擾方法給出初步解釋。同時也可以看到在微擾理論的框架下,計算出的電阻等物理量在低溫區(qū)總是發(fā)散。這不符合實驗結(jié)果。這就迫使我們必須去尋找非微擾方法。第三章主要是闡述幾種非微擾方法。為此我們先討論了贗費米子表示和微擾重整化群。接著我們詳細給研究了非微擾重整化的理論方案以及Bethe ansatz嚴格解方法。在第四章中,我將針對低溫強耦合區(qū)建立一個有效理論。我們發(fā)現(xiàn)在強耦合區(qū)可以用一個弱耦合的朗道費米液體理論來刻畫這個不動點。這種特定能標下的有效理論正是重整化群思想的核心。從第五章起至第八章,我主要討論了近藤效應在拓撲量子系統(tǒng)中的相關(guān)研究與應用。第五章主要是介紹當前在該領(lǐng)域的研究現(xiàn)狀。第六章到第八章分別是三個具體的研究實例。從這些章節(jié),我們可以看到,近藤效應盡管是一個已經(jīng)有半個多世紀歷史的研究課題,當它和新的拓撲態(tài)系統(tǒng)相結(jié)合后,不僅會展現(xiàn)出與傳統(tǒng)近藤效應不同的物理特征,同時也可能產(chǎn)生出更多新穎的拓撲量子態(tài)。
[Abstract]:Since -40s, Kondo effect and its related physical problems have been an important research hotspot in condensed matter theory. Moreover, a series of numerical methods based on renormalization groups have been developed. On the other hand, in recent years, due to their potential applications in quantum transport and topological quantum computing, Topological quantum state matter has gradually developed into one of the most important research topics in condensed matter physics. One interesting and practical question in theory is: what new physics will the traditional Kondo effect produce in a novel topological quantum phase? Kondo resonance, Kondo temperature and so on will be different from the traditional metal Kondo effect? Is it possible to induce a new topological quantum state by the formation of a single state of Kondo? Once combined with the topological quantum system, The traditional Kondo question will produce a series of new and interesting questions related to it. The main purpose of this paper is to explore and answer these questions. In Chapter 1, I will give a brief overview of the two topics to be studied in this paper. From the perspective of studying history, I described its development process and reviewed the important progress in history. I mainly try to answer what topology is and how to depict the topological state. Chapter 2 is about the perturbation treatment of Kondo effect. First, I discuss the solution of T matrix for nonmagnetic impurity problem. Then I use T matrix method to solve the problem of nonmagnetic impurity. For Anderson model and s-d exchange model, We use the perturbation method proposed by Kondo to give a preliminary explanation. At the same time, we can see that in the framework of perturbation theory, The calculated physical quantities such as resistors always diverge in the low temperature region. This does not accord with the experimental results. This forces us to find non-perturbation methods. Chapter 3 mainly describes several non-perturbation methods. For this reason, we first discuss the pseudo-perturbation methods. Fermion representation and perturbation renormalization group. Then we study the theoretical scheme of nonperturbed renormalization and the Bethe ansatz rigorous solution method in detail. In Chapter 4th, We find that a weakly coupled Landau Fermi liquid theory can be used to characterize this fixed point in the strongly coupled region. From Chapter 5th to Chapter 8th, I mainly discuss the related research and application of Kondo effect in topological quantum system. Chapter 5th mainly introduces the current research situation in this field. Chapters 6th to 8th are three specific research examples. We can see that although the Kondo effect is a research topic with a history of more than half a century, when it is combined with the new topological state system, it will not only show different physical characteristics from the traditional Kondo effect. It is also possible to produce more novel topological quantum states.
【學位授予單位】：南京大學
【學位級別】：博士
【學位授予年份】：2017
【分類號】：O469

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