量子磁性体系中量子相变的理论研究

Quantum phase transitions (QPTs), which are induced by the change of coupling strength of the quantum fluctuations, occur at absolute zero temperature of an interacting quantum many-body system. Quantum spin systems are currently at the frontier of modern physics and advanced materials research. In this proposed project, the applicant will utilize both analytical and numerical expertise in many body physics to study the exotic quantum states and QPTs of quantum spin systems and to develop a better understanding of the underlying deep physics and experimental findings. In particular, we will focus on the following four cutting-edge topics in this area: .1)Exploring quantum states and QPTs in geometrically frustrated magnets. Recently we studied the quantum phases and QPTs in an interacting boson model on triangular lattice. We develop systematically a simple and effective way to use the vortex degree of freedoms on dual lattices to characterize both the density wave and valence bond symmetry breaking patterns of the boson insulating states. A novel insulating quantum state which has both density wave and valence bond solid orders is obtained. Recent experimental data revealed a series of new insulating state in 3D Pyrocholre magnets and up to now it is still lack of theoretical explanations. We will work on the nature of those states..2)Topological invariants characterization of quantum phase in low dimensional quantum magnets.QPT in transverse Ising model can be described by Landau's paradigm of symmetry breaking. We proposed a Z2 topological invariant which may characterize the QPT in such model. For real 3D materials, we need rely on numerical calculations like exact diagonalizations, DMRG and quantum Monte Carlo to treat the effect of interchain coupling. Moreover, we plan to study the Kitaev model. Though the quantum Monte Carlo is not good for it, we are developing other methods as well, such as the tensor network method which is generalization of the DMRG to higher dimensions..3)Impact of classical or quantum noises on the QPTs. Nonequilibrium effects at a QPT appear as an emerging ?eld both experimentally and theoretically. Recently we proposed a new approach to detect the quantum phase transitions by using classical noise detection. The quantum critical point of the transverse Ising model can be identified straightforwardly by examining the time evolution of magnetization in the presence of non-Markovian noise. We will study further more quantum systems and generalize our approach to quantum noises. .4)Interdisciplinary study between quantum information and QPTs. We will study a long standing fundamental but subtle problem in quantum information, many-particle quantum entanglement. Moreover we will explore the intrinsic relationship between the novel QPTs and quantum entanglement in quantum spin systems. The measure of quantum entanglement can include entanglement entropy, entanglement spectrum and emergent entanglement Chern number.

量子相变是在绝对零度下通过改变体系控制参数由量子涨落诱发的相变，该现象在凝聚态系统中广泛出现。其本身作为新的视角，提供了研究关联凝聚态中悬而未决的重要难题的途径。量子磁性体系是研究关联体系新奇量子现象的重要领域, 同时具有广泛的新型材料的应用前景。研究量子磁性体系中量子相变机制，发展能够实现量子调控的基础理论与当前实验前沿紧密相关。如在几何组错系统、具有拓扑物性的低维体系、非平衡效应对于量子相变的影响、量子信息与量子相变的交叉领域等相关量子磁性体系中量子相变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四个方面：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新奇量子态及量子相变；低维量子磁性体系中拓朴量子态的拓扑不变量描述及其量子相变研究；研究经典及量子噪音对于量子相变的影响，探索测量量子相变的新型方案；探讨从量子纠缠、纠缠谱等量子信息的角度深入理解量子相变。

量子相变是在绝对零度下通过改变体系控制参数由量子涨落诱发的相变，该现象在凝聚态系统中广泛出现。其本身作为新的视角，提供了研究关联凝聚态中悬而未决的重要难题的途径。量子磁性体系是研究关联体系新奇量子现象的重要领域, 同时具有广泛的新型材料的应用前景。研究量子磁性体系中量子相变机制，发展能够实现量子调控的基础理论与当前实验前沿紧密相关。本项目的研究集中在以下四个方向并取得进展: .1）在量子阻错磁性体系中的新奇量子态及其相变的研究方面，我们提出了在量子横场自旋梯子体系中产生、调控以及测量Majorana 费米子的理论方案；发展了新型的数值方法用来确定量子拓扑体系的简并态；首次在各向异性的量子组错磁性体系实现手征量子自旋液体状态；预言手征/非手征性的两种自旋液体态，之间为连续相变。.2）在拓扑物态量子特性的理论研究方面，我们研究了Sb2Se3在压力下发生从平庸的能带绝缘体到拓扑绝缘体的拓扑量子相变的机制；理论预言分数Chern 绝缘体可能在二维有机金属材料中实现;建议在具体的哈密顿体系中存在分数量子自旋霍尔态并证明在该体系中可能会出现电荷密度波的条纹相以及Tao-Thouless态；预言具有CT联合对称性的二维Weyl类型半金属等。.3）在超冷原子光晶格体系中的新奇量子态的理论研究方面，理论预言在组错晶格的相互作用玻色体系中存在密度波序与价键晶体序共存的新奇量子相；具有强自旋轨道耦合的极化费米超流体系中，我们理论得到陈数为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；理论预言拓扑超流体中磁性或非磁杂质在强散射极限下，能隙内出现普适性束缚态。.4）在发展量子多体计算的新方法方面，我们将张量网络态中的多层纠缠重整化(MERA)方法和场论中处理费米子问题的Grassmann 代数相结合，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。