三維類六邊形晶格的數值研究及磁化跳躍

Abstract

我們發展了一個研究多體物理的數值方法叫做精確對角化(Exact Diagonalization, ED)。這個方法可經由對角化漢彌爾(Hamiltonian)來計算各種物理觀測值。在第二章中我們將詳述這個方法的原理及實行。而在第三章中，我們將用精確對角化這個方法去探究先前在二維六邊形晶格上的一些奇異現象，如磁化跳躍。及用以解釋磁化跳躍這個不尋常現象的想法叫做局域磁子狀態(Localized Magnon State, LMS)。第四章我們將用精確對角化的方法去研究三維類六邊形晶格的基本性質，及探索是否也存在有磁化跳躍這樣的情形。

We develop a numerical method which is called exact diagonalization(ED) in our group. The method can exactly calculate various physical observables by diagonalizing the Hamiltonian. The ED methods will be discussed in Chap2. In Chap.3, we will perform some calculations such as the knight shift around single impurity in square lattice. And the properties of the kagome lattice such as magnetization to check our codes. We will also use ED method to caculate some properties of the hyperkagome lattice in Chap.4. We find some anomalous phenomena and some good properties in the hyperkagome lattice such as magnetization jump and the adiabatic demagnetization curve. We try to explain these phenomena by the localized magnon states which will be introduced in Sec.1.4.