关联拓扑量子态的理论研究

Quantum correlated systems are currently at the frontier of modern physics and advanced materials research. They are also the playground for exotic topological quantum states. During the past years, much interest has been attracted in this area including quantum spin liquid and anyon superconductivity, exotic states in layered organic conductors, the creation and manipulation of Majorana fermions in physical systems. In this proposed project, the applicant will utilize both analytical and numerical expertise in many body physics to study the exotic topological quantum states in quantum correlated systems and to develop a better understanding of the underlying deep physics and experimental findings. In particular, we will focus on the following three cutting-edge topics in this area. 1) Exploring chiral spin liquid and anyon superconductivity: Recently we showed that Kalmeyer-Laughlin chiral spin liquid exists in a frustrated anisotropic kagome Heisenberg model, which has spontaneously time reversal symmetry breaking. Our model has two topological degenerate ground states, which exhibit non-vanishing scalar chirality order and are protected by finite excitation gap. We will continue to find out more Hamiltonian systems which host chiral spin liquid by using numerical iDMRG and MERA techniques. Moreover, we will study the possible emergence of anyon superconductivity by doping the chiral spin liquid state. The nature of such exotic state will be further investigated. 2) Rich phase diagram of layered organic materials: Layered organic superconductors are on the verge of the Mott insulator. Recent experimental data revealed a series of new quantum states in such compounds and up to now it is still lack of systematic theoretical explanations. We will use the Gutzwiller variational method to study the rich phase diagram and exotic quantum states in terms of a Hubbard model including a spin exchange coupling term as a minimal model. By using exact diagonalization technique for finite system, we will study the possible realization of fractional Chern insulator in layered organic materials. 3) Majorana fermions in strongly correlated systems: We will propose theoretically the creation, manipulation and fusion of Majorana fermions (MFs) in two physical systems. In our previous study, we numerically showed that the MFs qubit state can be read out by measuring the fusion excitation in the quenched inhomogeneous spin ladders. An exactly solvable T-junction spin ladder model has been constructed non-Abelian braiding statistics has been verified. Moreover, we will work on more realistic models and study the dynamics of the physical processes. For the superconductor-topological insulator heterostructures, we will numerically study the impurity effect and magnetic field effect. The nature of vortex core states and its relevance to MFs will be investigated.

量子关联体系是研究新奇拓扑量子现象的前沿领域, 同时具有广泛的新型材料的应用前景。研究关联拓扑量子态及其量子相变机制，发展能够实现量子调控的基础理论是与当前实验前沿紧密相关的理论问题。如量子自旋液体及任意子超导电性、二维有机导体中的新奇物性、Majorana费米子态在量子关联体系的实现等关联拓扑量子态的理论研究成为当前凝聚态理论前沿研究的重要方向。本课题的研究将集中在以下三个方面：结合多种解析与数值手段研究具有几何组错反铁磁体中的时间反演自发破缺的手征自旋液体态以及空穴掺杂情形下的任意子超导态的产生及其新奇物性；研究二维有机物导体的丰富相图并深入探讨其相变，研究分数Chern绝缘体的可能实现；研究准一维量子磁性体系以及超导体与拓扑绝缘体异质结构，探讨该体系中实现Majorana费米子的产生、调控以及聚合的理论方案。

量子关联体系是研究新奇拓扑量子现象的前沿领域, 同时具有广泛的新型材料的应用前景。研究关联拓扑量子态及其量子相变机制，发展能够实现量子调控的基础理论是与当前实验前沿紧密相关的理论问题。本项目的研究集中在以下五个方向并取得进展: .1）在具有几何组错及强几何限制的量子磁性体系中的新奇量子态及其相变的研究方面，通过考察拓展的XXZ Kagome模型，得到体系不同参数下的手征自旋液体态及时间反演对称的自旋液体状态，两者之间的相变为连续相变。发展了新型sweeping cluster量子蒙卡算法适合于研究具有强几何限制的一类量子自旋模型，得到正方晶格QDM的基态相图。.2）理论研究了分数量子自旋Hall体系中不同自旋之间相互作用的效应，证明在该体系中可能会出现电荷密度波的条纹相。在torus的几何结构中得到了非平庸的分数拓扑的Tao-Thouless量子态。此外，在交错磁通的半满方格子体系中提出玻色子的关联跃迁模型，得到了无净磁通的玻色子整数量子霍尔态，作为Haldane模型在玻色体系中的对应。.3）在拓扑超导及超流态的理论研究方面，理论预言在手征P波超导体中的不同杂质态及磁通涡旋态的Majorana模式；具有强自旋轨道耦合的极化费米超流体系中，理论得到陈数为2的新型拓扑LO态，在有限掺杂情形得到5种具有拓扑属性的超流态；理论预言Bi／Ni双层体系超导态对应于He3超流体系中的ABM态，即具有节点的p波对称性；在NbSe2与CrCl3的范德华异质界面找到实现FFLO态的证据。.4）在高温超导电性的量子多体计算研究-GMERA算法研究t-J模型方面，发展出了一种普适而严格的处理二维关联电子模型的新型GMERA方法。在有限尺寸的二维正方晶格t-J模型中，首次得到了t-J模型基态为自发对称破缺的d波超导态；超导序参量与自旋密度波及电荷密度波共存；空穴掺杂超导增强而电子掺杂超导削弱。.5）在耗散环境下量子自旋系统的相变研究方面，提出了对环境建模以模拟其本质物理特性，考察耗散环境下一维XXZ自旋链在零温的相图，发现除了相变点会随着系统与环境耦合强度变化而移动；引入的耗散环境模式使得不可压缩态进入可压缩状态，还使得一维系统产生了热力学相变。得到二维XY模型在Calderia-Leggett耗散影响下的体系相图，特别是在几个相边界附近关联函数的特性，以检验关于局域临界特性的理论。