低维阻挫量子磁性系统及非传统拓扑相变的研究

拓扑序是一种高度非平庸的具有长程量子纠缠的量子态。量子自旋液体是一种重要的拓扑序，源于低维系统中强关联、强阻挫效应和量子涨落等因素之间的竞争。随着自旋阻挫新材料的不断出现，量子自旋液体已发展成为凝聚态物理最重要的研究前沿领域之一。. 另一方面，基于数值计算和物性研究，有迹象表明一些自旋阻挫体系存在一种从具有对称性破缺的传统相到拓扑序的相变。然而，关于这类非传统相变，目前还缺乏一个较为完善和统一的理论。本项目将基于自旋阻挫体系的进展，从微观模型出发，一方面，发展算法、提高效率与精度，检验这种拓扑序及其相变，深入研究基态简并性、任意子统计和拓扑纠缠熵等拓扑序的基本特性。另一方面，基于现有积累，发展比施温格玻色子、费米子平均场方法更有效的新解析方法，研究拓扑序及其相变的物理机制。通过高精度数值计算和解析费米化研究的紧密结合，针对几类非传统拓扑相变，构建一套超越传统朗道对称性破缺范式的相变理论。

Topological orders are exotic quantum states with long-range quantum entanglement. Quantum spin liquids are one type of topological orders stabilized usually in low dimensional system due to the competition among the strong correlation effect, the strong frustration and quantum flucutations. With the discovery of new spin frustrated materials, quantum spin liquids have become one of the topical fields in condensed matter physics.. On the other hand, numerical and experimental studies have revealed that there exists some unusual phase transitions from the conventional symmetry breaking phases to topologically ordered phases in some spin frustrated models. However, a comprehensive and general theory on such unconventional phase transitions is still missing. This project, based on the most recent developments on frustrated spin systems, firstly aims to develop new numerical methods with high efficiency and accuracy to test and observe the topological orders and their phase transitions. The relevant study will focus on the topological behaviors such as the ground state degeneracy, the anyonic statistics, the topological entanglement entropy, etc. Then, based on our previous studies, the project aims to develop new analytic method that is more advantageous than the Schwinger boson, fermion mean-field. With the combination of high precision numerical simulations and the analytical fermionization approach, it is possible to construct a general theory applicable to some types of unconventional phase transitions that are beyond Landau's symmetry breaking paradigm.