量子磁体中的演生现象

Quantum magnets are strongly correlated electronic systems where quantum spin fluctuations dominate their low energy physics, which exhibit rich emergent phenomena. Namely, new particles and fields emerge at low energy scales but they are totally absent in the Hamiltonian describing the initial system. We shall study such emergent phenomena starting from both microscopic models and phenomenological theory. Microscopic theory is essential for understanding emergent phenomena and phenomenology plays an irreplaceable role in comparing theory with experimental data. The research will cover nonlinear sigma models on frustrated lattices, quantum spin systems with spin S>1/2, and phenomenological theory for quantum spin liquids. We shall derive different nonlinear sigma models with topological terms on frustrated lattices. Then we shall apply large N expansion and renormalization group to study competition between different Neel orders in these models and obtain phase diagrams based on quantum field theory. We shall study quantum spin systems with spin S>1/2. Project symmetry group analysis will be carried out to classify ground states for spin S=1 systems in triangular, honeycomb and kagome lattice. With the help of Gutzwiller wave functions and variational Monte Carlo method, we shall study the antiferromagnetic phases for spin S=1 magnets on the above lattices. We shall also generalize AKLT state to higher dimensions with spin S>1/2 using Majorana fermion and parafermion. We shall generalize our newly proposed phenomenological theory for U(1) quantum spin liquids. Singe electron Green's function and collective modes will be investigated utilizing bosonization technique. The spin-orbit coupling will be introduced and its physical consequences will be considered. We shall study how the strong charge fluctuations will affect spin dynamics in Mott insulators in the vicinity of metal to insulator transition. We shall generalize the phenomenological theory to the situation when Dirac nodes are present in the spinon dispersion and to study Z2 spin liquids with spinon pairing. We shall also study how to derive the phenomenological theory starting from microscopic models.

量子磁体是一类特殊的电子强关联系统，自旋的量子涨落主导了低能物理特性。其中存在丰富的演生现象，在较低的能量尺度上呈现出原始系统中没有的新粒子与场。我们将从微观模型与唯象理论出发来研究这些现象。 研究阻挫晶格上的非线性σ模型。推导阻挫晶格上的非线性σ模型及其拓扑项；用大N展开与重整化群的方法研究各种Neel序之间的竞争，得到基于量子场论的相图。 研究自旋S>1/2的量子自旋系统。用投影对称群对三角、六角、kagome晶格上的S=1的反铁磁系统进行分类；用变分蒙特卡洛方法通过投影波函数来研究这些反铁磁相；将AKLT态推广到高维高自旋系统。 研究量子自旋液体的唯象理论。研究单电子格林函数与集体激发模式；研究自旋-轨道耦合的物理效应；研究Mott绝缘体中电荷涨落对自旋动力学的影响；将理论推广到具有Dirac点的情况；研究spinon配对产生的Z2 自旋液体；研究如何从微观模型导出唯象理论。

在本项目中，我们研究了量子多体系统中的演生现象，包括：量子自旋液体、关联拓扑系统、低维系统的磁性与超导、量子自旋霍尔效应、拓扑超导中的Majorana零能模等。. 量子自旋液体：（1）研究三角晶格反铁磁J1-J2模型对应的非线性σ模型；（2）研究自旋S=1的链模型中的激发谱；（3）根据已有的量子自旋液体候选材料的实验发展，提出系统理论研究金属-量子自旋液体相变；（4）应邀为《Reviews of Modern Physics》撰写了量子自旋液体方面的综述论文。. 关联拓扑系统：（1）成功发现了相互作用Kitaev链模型在对称情况下的严格解，得到了基态相图及量子相变的临界特性，发现了拓扑态与拓扑平庸态之间的对偶对称性。（2）用Anderson杂质模型与变分方法研究三维Weyl拓扑半金属与Dirac半金属中的磁性杂质带来的Kondo效应。. 低维系统的磁性与超导：（1）在理论上研究了准一维新型超导体K2Cr3As3：通过构造分子轨道的方法，建立该类材料的微观模型，用无规相近似（RPA）方法研究超导的配对对称性。（2）用玻色化与重整化群方法分析了三轨道Luttinger液体的不稳定性，并将其应用到K2Cr3As3。（3）用平均场和行列式量子蒙特卡洛(DQMC)的方法研究了双层二维蜂窝晶格中的磁特性及其电场调控。. 量子自旋霍尔效应：我们研究了二维二维拓扑绝缘体InAs/GaSb量子阱（1）少量Si掺杂的量子阱的电子局域化与带间电子态；（2）电场控制的能带反转；（3）面内磁场与外加张力对电导量子化平台的影响；（4）面内磁场诱导的拓扑电荷密度波与自旋密度波。. 拓扑超导中的Majorana零能模：与实验组合作，我们研究了二维拓扑超导体（Bi2Te3/NbSe2异质结）涡旋中心的Majorana零能模，及其带来的自旋选择的Andreev反射。