有限温度张量重正化群方法及其在阻挫量子磁性研究中的应用

阻挫量子磁体中的新奇物态与效应是凝聚态物理研究的重要前沿方向，因其与高温超导、拓扑量子计算等的密切联系，近年来吸引了人们浓厚的研究兴趣。实验上，阻挫自旋液体候选材料的新进展层出不穷，人们系统地研究了若干三角晶格、笼目晶格和六角Kitaev 阻挫磁体等材料，发现其在一定条件下展现出自旋液体态的特征，但澄清其中的量子物态是充满挑战的量子多体问题。作者最近的工作指出，可以从有限温度张量重正化群多体计算入手，开展热力学性质的精确计算与分析，确定阻挫磁体的微观自旋模型，做出进一步理论预言并开展实验验证，从而建立量子磁性系统的多体计算精确研究方案。有限温度张量重正化群方法是计算大尺寸二维阻挫量子自旋模型有限温度性质的有力工具，在本文中作者首先介绍新近发展的系列张量重正化群方法，包括线性和指数张量重正化群等。随后，作者讨论有限温度张量方法在三角晶格量子伊辛磁体TmMgGaO4 和六角晶格Kitaev 磁体α-RuCl3 的微观自旋模型中的具体应用：通过高精度和全面的多体计算，揭示出其中存在演生U(1) 对称性与拓扑相变，以及高场量子自旋液体态等新颖的结论，这些理论预言也陆续被实验所证实。通过上述实例，作者展示了有限温度张量重正化群计算方法在自旋液体候选材料研究中的应用价值，并期待这些方法能在强关联量子物质研究中发挥重要作用。

Finite-Temperature Tensor Renormalization Group Method and the Applications to Frustrated Quantum Magnets#br#

The exotic spin states and quantum effects in frustrated magnets have attractedintensive research interest in recent years, which also have intimate connections with hightemperaturesuperconductivity and topological quantum computing, etc. Experimentally, peoplehave focused on typical spin liquid candidate materials including the triangular-, kagomeandKitaev honeycomb-lattice frustrated magnets. However, it constitutes a very challengingmany-body problem to clarify the quantum states and phase transitions therein. Recently, wepoint out that it is possible to establish a protocol for understanding and explaining experimentsof frustrated magnets in an unbiased manner. By employing the finite-temperature tensorrenormalization group methods, we carry out accurate calculations and analyses of thermodynamicproperties, determine the microscopic spin model of the frustrated magnets, andmake further theoretical predictions. Below, we firstly introduce the recently proposed tensorrenormalization group (TRG) methods, including the linear and exponential TRG, and discusstheir applications on the triangular-lattice quantum Ising magnet TmMgGaO4 and the Kitaevhoneycombmaterial α-RuCl3. We demonstrate that the finite-temperature TRG approachesshed light on the study of spin liquid candidate materials, and could facilitate cutting-edgeresearch in the field of strongly correlated quantum systems.