Study on the ground state of bilayer quantum Hall systems

本研究的目的是阐明基态、激发光谱、基态电流随层间距、隧穿强度、自旋塞曼分裂的变化规律。研究方法有解析法、精确对角化法和密度矩阵重整化法。本研究的目的之一，也是发展双层系统的DMRG程式。我们得到了以下结果：1.双层系统，其中总填充是一个整数，每层的朗道量子数不同。在这种情况下，当层指数由pseudospin表示时，系统由类伊辛模型描述。阐明了在一定的间距下，可以实现两种不同的密度波态，这两种密度波态是由密度波的相对相位来区分的。在这种情况下，基态具有各种可能性，包括复合费米子的Halperin的331态、Pfalanan态、条纹态和费米液态，这取决于层分离、每层的厚度和隧穿强度。阐明了在一定的间距和厚度下，基态随隧穿强度的变化是连续演化的，而最低激发态从准粒子态到非阿贝尔统计态的变化是不连续的。这种转变解释了实验上观察到的奇怪行为。3.双层体系DMRG程序的开发：DMRG方法在二维体系中的应用并不明显。我们将我们成功的单层系统DMRG程序扩展到双层系统。目前正在利用这一程序研究双层体系。4.在足够大的分离下的行为。阐明了实现条纹态的条件。阐明了散粒噪声实验中观察到的“电荷”的含义。

The object of this study is to clarify how the ground state, excitation spectrum, funneling current develop as interlayer distance, tunneling strength, spin-Zeeman splitting are changed. The methods of study are analytical method, exact diagonalization, and density matrix renormalization (DMRG) method. The development of program of DMRG for the case of bilayer systems is also one of the object of this study. For these objectives we obtained the following results.1.Bilayer systems in which total filling is an integer with different Landau quantum numbers for each layer. : In this case the system is described by an Ising like model, when the layer index is expressed by pseudospin. It is clarified that at certain separation two types of density wave states are realized distinguished by relative phase of the density wave.2.Bilayer system at filling one-half. In this case the ground state has various possibilities that include 331 state by Halperin, Pfaffian state, stripe state and Fermi liquid state of composite fermions, depending on the layer separation, thickness of each layer, and tunneling strength. We clarified that for certain separation and thickness corresponding to an experiment, the ground state evolves continuously as tunneling strength is varied, but the lowest excitation change discontinuously from ordinary quasiparticle state to that with non-abelian statistics. This transition explains the strange behavior observed experimentally.3.Development of DMRG program for bilayer systems : It is not obvious to apply DMRG method to two dimensional systems. We extended our successful DMRG program for singly layer system to bilayer systems. Research of bilayer systems using this program is presently underway.4.Behavior at large enough separation. We clarified conditions for realization of stripe states. The meaning of "charge" observed by shot noise experiments is clarified.