二维阻挫自旋液体材料基态性质的大规模密度矩阵重整化群研究

Quantum spin liquid is a novel quantum state of matter found in frustrated antiferromagnets, which does not show any magnetic order or lattice crystal order even at zero temperature because of strong quantum fluctuations. Spin liquid states possess massive quantum entanglement and exotic fractionalized excitations. Such states have been considered to play important roles for understanding strongly correlated systems such as high-temperature superconductors, as well as for realizing topological quantum computation. In the past years, extensive research has been focused on the kagome material herbertsmithite and the spin-1/2 kagome Heisenberg model, which shows very strong geometric frustration. Recently, spin-liquid-like behaviors have also been observed in experiment for several materials with other geometric structures, including the Kitaev honeycomb material RuCl3, the triangular material YbMgGaO4, YbZnGaO4, and the double-layer kagome material Ca10Cr7O28. Besides the extensively studied frustration effects, new mechanisms including spin-orbital coupling, layer coupling, magnetic field, and disorder may play important roles for realizing the spin liquid physics in these materials. In this project, we plan to implement the large-scale density matrix renormalization group to study the ground-state properties of these new materials, including the static and dynamic properties. We would focus on the interplay between frustration and the effects of spin-orbital coupling, layer coupling, magnetic field, or disorder, as well as their affections on the possible spin liquid states in these materials. Furthermore, we would also compare theoretical results with experimental data, looking for the physical mechanisms that drive the spin liquid physics in the materials. Our project would not only help to understand the low-temperature properties of the new spin-liquid-like materials, but also shed more light on how to realize spin liquid states in real materials.

自旋液体是阻挫磁性系统里发现的新奇量子物态。在阻挫和量子涨落的作用下，自旋液体表现出无序行为。自旋液体有很强的量子纠缠和奇异的分数激发，对于理解相关强关联系统和实现拓扑量子计算有重要意义。该领域过去的研究主要集中在高阻挫的kagome系统。最近，几类具有其他结构的新型材料也表现出类似自旋液体行为，包括Kitaev honeycomb材料RuCl3，三角格子材料YbMgGaO4和双层kagome材料Ca10Cr7O28。除了研究较多的阻挫效应，自旋轨道耦合，层间耦合，无序等因素在这些材料里可能起到重要作用。本项目将采用大规模密度矩阵重整化群方法研究这几类材料的基态性质。重点研究自旋轨道耦合，层间耦合，磁场，以及无序对形成自旋液体的影响；同时将结合实验结果分析材料出现类似自旋液体行为的物理机制。本项目不仅有助于理解这些材料的低温物理性质，也能让我们对于如何形成自旋液体有更广泛深刻的认识。

该项目拟针对量子自旋液体研究中几类具有一定重要研究意义的微观自旋模型开展大尺度密度矩阵重整化群计算，期望对相关的理论研究和进一步实验研究提供参考和新的思路。主要研究内容包括：1. Kitaev家族模型在磁场下的自旋液体性质的理论研究；2. 二维阻挫系统中无序所诱导的新奇物态；3. 自旋1/2的正方格子和三角格子阻挫系统中的自旋液体态；4. 自旋1的正方格子系统中的向列序和自旋液体态；5. 发展计算基态性质的张量重整化群方法；6. 掺杂自旋液体态。重要结果包括发现和描述了Kitaev家族模型在外磁场下的自旋液体中间相；首次在二维阻挫海森堡模型中发现无序诱导的类似于一维无序系统中random singlet态的新奇物态；通过张量重整化群计算在大尺度上刻画了正方格子海森堡模型中的无能隙自旋液体相，指出该自旋液体相可能与其附近的解禁闭量子临界行为存在潜在关系；发现了三角格子系统中由电荷涨落导致的手征自旋液体相，描述了三角格子海森堡模型新奇的热力学行为；发现了自旋S=1系统中的自旋液体并刻画了系统中的向列序，首次在微观模型中发现了拓扑序与传统磁有序的共存；在大尺度计算中确认了掺杂正方晶格上的莫特绝缘体可以得到稳定的d波超导态。这些结果对于理解基本磁性系统的物理性质和寻找自旋液体具有一定的推动作用。