关联拓扑量子态的理论研究

项目名称： 关联拓扑量子态的理论研究

项目编号： No.11474064

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 陈焱

作者单位： 复旦大学

项目金额： 90万元

中文摘要： 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。

中文关键词： 自旋液体；超导电性；拓扑物态；新奇量子态

英文摘要： 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.

英文关键词： spin liquid;superconductivity;topological matter;novel quantum states