有阻挫量子体系新奇量子物态及量子相变理论研究

Due to the strong quantum fluctuations induced by the frustration, the low-dimensional quantum systems exhibit various exotic and novel quantum phenomena and rich phase diagrams. Therefore, they provide us a good platform to search for some exotic quantum states and carry out the investigations of quantum phase transitions. By the density-matrix renormalization-group method and the tensor network algorithms, combined with some analytical techniques, we would like to: (1) investigate the ground-state properties and phase diagram of some low-dimensional quantum systems; (2) discuss the reason and mechanism of quantum phase transitions and exotic and novel qantum states; (3) study quantum phase transitions in quantum systems by the nonanalytical behavior of quantum entanglement and fidelity, and try to obtain an efficient approach to deal with quantum many-body problem and to describe quantum phase transitions from the point of view from quantum information theory. Both the exploration of the exotic and novel quantum states and quantum phase transitions are important topices in condensed matter theory. All these investigations may provide a more comprehensive understanding of the exotic and novel phenomena in quamtum systems, and accelerate the development of condensed matter theory and its related subjects.

低维有阻挫量子体系由于其强烈的量子涨落而呈现出奇异量子现象和丰富的物理相图，从而为新奇量子物态和量子相变的研究提供了一个平台。本项目拟采用密度矩阵重整化群和张量网络态算法，结合解析手段进行以下研究：(1)研究低维有阻挫量子体系的基态物理特性及其相图；(2)探讨引发量子相变和新奇量子物态的原因和物理机制；(3)利用量子纠缠和保真度等在临界点附近所表现出的奇异行为描述量子相变，探索用量子信息的手段研究量子多体问题并探索描述量子相变的有效方法。新奇量子物态的探索及量子相变研究都是当前凝聚态理论的重要课题。本项目的这些研究有助于加深人们对有阻挫量子体系新奇量子现象的认识，并将促进凝聚态理论及其交叉学科的发展。

在项目的资助下，我们对一系列一维量子体系进行了研究，详细讨论了这些体系中的量子相变，得到了这些模型的基态相图，探讨了各种相互作用引发的新奇量子物态。本项目的这些研究有助于加深人们对有阻挫量子体系新奇量子现象的认识，并将促进凝聚态理论及其交叉学科的发展。项目组成员掌握并熟练应用基于矩阵乘积态框架下的密度矩阵重整化群(DMRG)和无限时间演化块消减(iTEBD)算法，能够处理一维量子体系热力学性质的LTRG算法，能够处理研究树状的Bethe格子算法。这些数值计算方法为我们进一步开展研究工作（或研究其他一些有趣的量子体系）提供了必要的工具。迄今为止，我们共发表SCI论文23篇，4名研究生顺利毕业。