通往量子自旋液体的新路径——Kitaev模型的材料实现

Kitaev模型是一种建立在二维六角蜂窝状格子上的有效自旋为1/2的量子自旋液体模型。该模型可严格求解,具有拓扑序,分数化激发产生马约拉纳费米子与Z_2规范场,提供了对拓扑物理学与非易失性存储技术研究的新思路。区别于三角晶格与笼目格等材料中由于几何阻挫导致的量子自旋液体态,Kitaev量子自旋液体的形成来源于自旋空间中各向异性的Kitaev相互作用。近年来,在真实材料体系中寻找这种相互作用成为了实现量子自旋液体的新途径。其中,具有六角蜂窝状结构的莫特绝缘体α-RuCl_3被认为是众多候选材料中最具潜力的一种。文章将从实验角度出发,以α-RuCl_3为主要代表体系,介绍近年来在Kitaev量子自旋液体实验研究方面的重要进展,特别是以中子散射为主要手段对材料中与Kitaev量子自旋液体态相关的自旋激发态研究的结果。     

量子自旋液体的实验研究进展

量子自旋液体是指由于其中存在的强量子涨落导致自旋即使在零温极限下也不形成磁有序的一种新的自旋量子态。区别于传统的磁有序材料,它的基态没有确定的序参量来表示,并且不伴随任何自发的对称性破缺,超越了朗道相变理论所能描述的物相范畴,代表了一种新奇的量子物态,具有非常高的理论研究价值。这一全新的物态被认为与非常规超导机制之间有着十分紧密的关系。同时在未来的量子计算方面有着非常诱人的应用前景,因此一直以来备受关注。虽然量子自旋液体理论经过近半个世纪的积淀有了长足的发展,但是由于候选材料稀少,实验测量条件苛刻等多种因素制约,导致实验方面的进展相对缓慢。近年来各项实验技术的进步和成熟为量子自旋液体候选材料的测量表征提供了有利条件,加快了实验工作的推进速度。本文将从实验的角度介绍 (1) 几何阻挫量子自旋液体候选材料,包括三角晶格化合物 YbMgGaO量子自旋液体是指由于其中存在的强量子涨落导致自旋即使在零温极限下也不形成磁有序的一种新的自旋量子态。区别于传统的磁有序材料,它的基态没有确定的序参量来表示,并且不伴随任何自发的对称性破缺,超越了朗道相变理论所能描述的物相范畴,代表了一种新奇的量子物态,具有非常高的理论研究价值。这一全新的物态被认为与非常规超导机制之间有着十分紧密的关系。同时在未来的量子计算方面有着非常诱人的应用前景,因此一直以来备受关注。虽然量子自旋液体理论经过近半个世纪的积淀有了长足的发展,但是由于候选材料稀少,实验测量条件苛刻等多种因素制约,导致实验方面的进展相对缓慢。近年来各项实验技术的进步和成熟为量子自旋液体候选材料的测量表征提供了有利条件,加快了实验工作的推进速度。本文将从实验的角度介绍(1)几何阻挫量子自旋液体候选材料,包括三角晶格化合物YbMgGaO_4和YbZnGaO_4、κ-(BEDT-TTF)_2Cu_2(CN)_3、EtMe_3Sb[Pd(dmit)_2]_2和kagome格子化合物ZnCu_3(OH)_6Cl_2;(2)Kitaev量子自旋液体候选材料铱氧化物(Na_2IrO_3与α-,β-,γ-Li_2IrO_3)和α-RuCl_3。文章将着重介绍近年来在量子自旋液体实验方面的进展,之后做一个简单的总结,最后对量子自旋液体的未来发展做一个展望。     

自旋阻挫重费米子体系中的量子相变

近藤效应和RKKY交换相互作用的竞争决定了多数重费米子化合物的基态性质。通过压力、磁场等非热力学参量调控,该类材料能够在绝对零温附近实现费米液体和磁有序相之间的连续转变,提供了研究量子相变的理想平台。另一方面,在绝缘的量子磁体中,自旋阻挫引起的量子涨落抑制低温下长程磁有序的发生,导致自旋液体相等新奇物态的产生。在近藤晶格中引入自旋阻挫将给重费米子材料提供一个新的调控维度,深刻改变该类材料的量子临界相图,是重费米子材料领域的一个新颖研究方向。文章首先介绍阻挫重费米子体系的研究背景,然后针对Ce Pd Al的物性展开讨论,探讨阻挫对重费米子材料量子临界物性的影响以及量子临界相的普适性。     

量子自旋液体候选材料的缪子自旋弛豫研究

量子自旋液体是一种新奇的磁性物态。由于极强的量子涨落，直至零温都不会出现长程序。量子自旋液体的基态不能用序参量描述，并且缺少对称性破缺，因此该物态的实现打破朗道理论的范式。对于量子自旋液体的研究有助于理解高温超导的机理，并且可以被应用在量子计算和量子信息中。目前，尽管理论上有了长足的发展，但仍旧没有任何一个材料被证实为量子自旋液体。因此，探测和确认一个真正的量子自旋液体材料是当前的研究重点。缪子自旋弛豫是一个对磁场极为敏感的实验技术，被广泛应用于量子自旋液体候选材料的研究中。该技术可以观测基态中是否存在磁有序，测量系统中的涨落频率，这两点都是表征量子自旋液体的重要性质。本文简要介绍了量子自旋液体态和缪子自旋弛豫技术，回顾了近期在不同体系的量子自旋液体候选材料中的实验结果，特别是缪子自旋弛豫的成果。这些体系包括一维反铁磁海森堡链（苯甲酸铜），三角格子（YbMgGaO4，NaYbO2 和TbInO3），笼目格[ZnCu3(OH)6Cl2 和 m3Sb3Zn2O14]，蜂窝状格子（Na2IrO3 和 α-RuCl3），以及烧绿石结构（Tb2Ti2O7，Pr2Ir2O7 和Ce2Zr2O7）。     

有限温度量子多体系统与热态张量网络

量子多体系统热力学性质的精确模拟在理论和实验方面都具有重要的价值。局域相互作用量子多体系统的热态满足互信息(mutual information)面积律,对于这样的系统,热态张量网络可以提供满足面积律的精确"波函数"拟设,提供了模拟有限温度系统的有力手段。文章介绍了关联格点模型在有限温度下的热态张量网络刻画及相关模拟方法。作者按照世界线热态张量网络和级数展开热态张量网络来分别介绍,并讨论了自由能极小变分原理与重正化群剪裁的优化原则。世界线框架内,人们发展了转移矩阵重正化群,基于纯化策略的有限温度密度矩阵重正化群,以及张量网络的线性重正化群等方法。在此基础上,介绍作者新近提出的级数展开热态张量网络方法,该方法受随机级数展开量子蒙特卡罗方法的启发,突破了世界线方法的局限,提高了有限温度计算重正化群模拟的精度标准,并且在计算阻挫量子自旋链模型时不会有负符号问题。此外,文章讨论了在两维格点系统上推广有限温度张量网络计算的进展和未来展望。     

磁体“沙漠”中的月牙泉——量子自旋液体

当温度趋于零时,如果阻挫自旋系统不呈现长程磁序也不破缺晶格对称性,而且其低能物理性质表现出分数化的量子特征,这种状态称为量子自旋液体态。量子自旋液体随着高温超导的发现而被大量研究,它超越了朗道对称自发破缺的理论框架,并促进了拓扑序理论的发展,其分类理论是以投影对称群为代表的现代数学工具。量子自旋液体中的元激发是分数化的自旋子和演生规范场的光子或量子化磁通,有能隙的量子自旋液体可应用于拓扑量子计算。研究量子自旋液体的理论工具还包括严格可解格点模型、各种不同的数值计算方法和量子场论等。实验上,三角晶格、笼目晶格、六角晶格甚至三维格点系统中的量子自旋液体候选材料相继被发现和深入研究,探测手段包括核磁共振、中子散射、热输运等,调控方法包括高磁场、高压强等。确切的量子自旋液体材料的寻找仍在持续进行中,近些年发展尤其迅速。中国研究人员做出了很多努力,并在部分方向上逐步开始起引领作用。量子自旋液体是一个充满困难和挑战的研究领域,也是一个充满魅力和活力的领域。     

二维量子磁晶体中的“幽灵软模”与KT物理

正通过大尺寸的量子多体热力学与动力学计算,来自北京航空航天大学、复旦大学、中国科学院物理研究所和香港大学的研究团队,成功"破译"了二维阻挫磁性晶体TmMgGaO_4(TMGO)的"材料基因"——三角晶格量子伊辛模型及其精确模型参数~([1])。籍此,研究者预言指出,磁性晶体TMGO将在特定的温度范围内展现出Kosterlitz—Thouless(KT)相。此前人们在二维超流和超导中观察到KT相变,而此项理论工作首次在实际二维磁性晶体中预言了KT物理的存在。通过分析自旋谱发现了三角晶格反铁磁体中存在类似     

阻挫诱导的亚铁磁性Heisenberg系统中的量子相变

利用密度矩阵重整化群(DMRG)方法研究磁性阻挫对一种S=1/2准一维反铁磁自旋链但却具有亚铁磁性的Heisenberg系统基态的影响.计算了单个晶胞的基态能、自旋关联函数以及自旋能隙.研究表明这种Heisenberg自旋系统的基态随着阻挫α的增强将从磁有序相变化到自旋无序相,并且伴随着自旋能隙的出现,量子相变点为α≈0.412.同时线形链上格点间自旋长程关联值的计算结果表明在磁有序区间体系的磁有序性质随着α的增强而减弱,阻挫在0≤α< 关键词： 准一维反铁磁自旋链 亚铁磁性 密度矩阵重整化群 自旋能隙     

强关联电子系统中的热输运测量

当考虑电子间的库伦排斥相互作用,以及电荷、自旋和轨道之间的相互耦合时,诸多超越 了近自由电子框架的新奇量子态涌现而出,如非常规超导态和量子自旋液体等。对这些新奇物态 的认知不仅会拓展现有的知识框架,也有望引发新一轮的量子科技革命。因此,对强关联物理的 研究是当下凝聚态物理领域的前沿课题。铜基高温超导体的母体是一种莫特绝缘体,在传统的能 带论之下被预言为金属态。然而电子间的强关联行为使得它表现出绝缘体的性质。由于莫特绝缘 体中库伦相互作用致使能隙打开并冻结其中的电荷自由度,所以在该体系中难以开展电输运性质 的测量研究。作为一种对于元激发（不仅包括电子,还包括磁振子、自旋子等）敏感的探针,热输 运测量在强关联电子系统的研究中发挥着重要的作用。本文回顾了近些年在非常规超导、重费米 子系统和量子自旋液体研究中一些有趣的纵向热输运性质的研究成果,并与我们近期发表的运用 横向热导率测量热霍尔现象的综述文章相互补充。      

扰动对有机磁体器件自旋极化输运特性的影响

基于紧束缚模型和格林函数方法,研究了有机磁体晶格扰动和侧基自旋取向扰动对金属/有机磁体/金属三明治结构有机自旋器件自旋极化输运特性的影响.计算结果表明:晶格扰动的存在降低了器件的起始偏压,减小了导通电流,并使得电流-电压曲线的量子台阶效应不再显著,扰动不太强时电流仍呈现较高的自旋极化率;而侧基自旋取向扰动减小了体系的自旋劈裂,增加了器件的起始偏压,低偏压下随着扰动的增强器件电流及其自旋极化率明显降低.进一步模拟了温度对器件自旋极化输运的影响. 关键词： 有机自旋电子学 有机磁体 自旋极化输运 自旋过滤     

Frontiers in frustrated magnetism

This article discusses at a qualitative level a number of issues at the forefront of current understanding and developments in frustrated quantum magnetism. The focal point of the presentation is the spin liquid, which is introduced in terms of (un)broken spin and lattice symmetries. An overview of the full spectrum of research activity in the field is obtained by considering selected examples from experimental approaches to realising spin-liquid states, from theoretical efforts which seek both to classify spin liquids according to their physical properties and to broaden the search for spin-liquid behaviour, and from numerical techniques which offer the prospect of qualitatively new insight into frustrated spin systems.     

Learning the Effective Spin Hamiltonian of a Quantum Magnet

To understand the intriguing many-body states and effects in the correlated quantum materials,inference of the microscopic effective Hamiltonian from experiments constitutes an important yet very challenging inverse problem.Here we propose an unbiased and efficient approach learning the effective Hamiltonian through the many-body analysis of the measured thermal data.Our approach combines the strategies including the automatic gradient and Bayesian optimization with the thermodynamics many-body solvers including the exact diagonalization and the tensor renormalization group methods.We showcase the accuracy and powerfulness of the Hamiltonian learning by applying it firstly to the thermal data generated from a given spin model,and then to realistic experimental data measured in the spin-chain compound copper nitrate and triangular-lattice magnet TmMgGaO_4.The present automatic approach constitutes a unified framework of many-body thermal data analysis in the studies of quantum magnets and strongly correlated materials in general.     

Quantum ice: a quantum Monte Carlo study

Ice states, in which frustrated interactions lead to a macroscopic ground-state degeneracy, occur in water ice, in problems of frustrated charge order on the pyrochlore lattice, and in the family of rare-earth magnets collectively known as spin ice. Of particular interest at the moment are "quantum spin-ice" materials, where large quantum fluctuations may permit tunnelling between a macroscopic number of different classical ground states. Here we use zero-temperature quantum Monte Carlo simulations to show how such tunnelling can lift the degeneracy of a spin or charge ice, stabilizing a unique "quantum-ice" ground state-a quantum liquid with excitations described by the Maxwell action of (3+1)-dimensional quantum electrodynamics. We further identify a competing ordered squiggle state, and show how both squiggle and quantum-ice states might be distinguished in neutron scattering experiments on a spin-ice material.     

Rare-Earth Chalcogenides: A Large Family of Triangular Lattice Spin Liquid Candidates

Frustrated quantum magnets are expected to host many exotic quantum spin states like quantum spin liquid(QSL), and have attracted numerous interest in modern condensed matter physics. The discovery of the triangular lattice spin liquid candidate YbMgGaO_4 stimulated an increasing attention on the rare-earth-based frustrated magnets with strong spin-orbit coupling. Here we report the synthesis and characterization of a large family of rare-earth chalcogenides AReCh_2(A = alkali or monovalent ions, Re = rare earth, Ch = O,S,Se). The family compounds share the same structure(R3 m) as YbMgGaO_4,and antiferromagnetically coupled rare-earth ions form perfect triangular layers that are well separated along the c-axis. Specific heat and magnetic susceptibility measurements on NaYbO_2,NaYbS_2 and NaYbSe_2 single crystals and polycrystals, reveal no structural or magnetic transition down to 50 mK. The family, having the simplest structure and chemical formula among the known QSL candidates, removes the issue on possible exchange disorders in YbMgGaO_4. More excitingly, the rich diversity of the family members allows tunable charge gaps, variable exchange coupling, and many other advantages.This makes the family an ideal platform for fundamental research of QSLs and its promising applications.     

Study of the spectral properties of spin ladders in different representations via a renormalization procedure

We implement an algorithm which is aimed to reduce the dimensions of the Hilbert space of quantum many-body systems by means of a renormalization procedure. We test the role and importance of different representations on the reduction process by working out and analyzing the spectral properties of strongly interacting frustrated quantum spin systems.     

Delta-Davidson method for interior eigenproblem in many-spin systems

Many numerical methods,such as tensor network approaches including density matrix renormalization group calculations,have been developed to calculate the extreme/ground states of quantum many-body systems.However,little attention has been paid to the central states,which are exponentially close to each other in terms of system size.We propose a delta-Davidson(DELDAV)method to efficiently find such interior(including the central)states in many-spin systems.The DELDAV method utilizes a delta filter in Chebyshev polynomial expansion combined with subspace diagonalization to overcome the nearly degenerate problem.Numerical experiments on Ising spin chain and spin glass shards show the correctness,efficiency,and robustness of the proposed method in finding the interior states as well as the ground states.The sought interior states may be employed to identify many-body localization phase,quantum chaos,and extremely long-time dynamical structure.     

Spin-1 pyrochlore antiferromagnets: Theory,model, and materials’ survey

Pyrochlore magnets can be a unique platform to demonstrate numerous important concepts and applications of frustrated magnetic physics in modern condensed matter physics. Most works on pyrochlore magnets deal with the interacting spin-1/2 local moments, while much less works have studied the spin-1 systems. We here review the physics with interacting spin-1 local moments on the pyrochlore lattice to illustrate the potentially interesting physics associated with spin-1 magnets. The generic pyrochlore spin-1 model includes the antiferromagnetic Heisenberg interaction, the Dzyaloshinskii– Moriya interaction and the single-ion spin anisotropy. The global phase diagram of this generic spin model is reviewed, and the relation between different quantum phases in the phase diagram is clarified. The critical properties of the transition from the parent quantum paramagnet to the proximate orders are discussed. The presence of quantum order by disorder in the parts of the ordered phases is analyzed. The elementary excitations with respect to the ground states are further reviewed, and the topological natures of these excitations are carefully addressed. The materials’ relevance of the spin-1 pyrochlore magnets are finally reviewed. This review may provide insights about the interesting spin-1 local moments on frustrated systems.     

Understanding spin configuration in the geometrically frustrated magnet TbB4: A resonant soft X-ray scattering study

The frustrated magnet has been regarded as a system that could be a promising host material for the quantum spin liquid (QSL). However, it is difficult to determine the spin configuration and the corresponding mechanism in this system, because of its geometrical frustration (i.e., crystal structure and symmetry). Herein, we systematically investigate one of the geometrically frustrated magnets, the TbB₄ compound. Using resonant soft x-ray scattering (RSXS), we explored its spin configuration, as well as Tb's quadrupole. Comprehensive evaluations of the temperature and photon energy/polarization dependences of the RSXS signals reveal the mechanism of spin reorientation upon cooling down, which is the sophisticated interplay between the Tb spin and the crystal symmetry rather than its orbit (quadrupole). Our results and their implications would further shed a light on the search for possible realization of QSL.     

Majorana's stellar representation for the quantum geometric tensor of symmetric states

Majorana's stellar representation provides an intuitive picture in which quantum states in high-dimensional Hilbert space can be observed using the trajectory of Majorana stars. We consider the Majorana's stellar representation of the quantum geometric tensor for a spin state up to spin-3/2. The real and imaginary parts of the quantum geometric tensor, corresponding to the quantum metric tensor and Berry curvature, are therefore obtained in terms of the Majorana stars. Moreover, we work out the expressions of quantum geometric tensor for arbitrary spin in some important cases. Our results will benefit the comprehension of the quantum geometric tensor and provide interesting relations between the quantum geometric tensor and Majorana's stars.     

低维纳米材料量子热输运与自旋热电性质 ——非平衡格林函数方法的应用

低维材料不断涌现的新奇性质吸引着科学研究者的目光. 除了电子的量子输运行为之外, 人们也陆续发现和确认了热输运中显著的量子行为, 如 热导低温量子化、声子子带、尺寸效应、瓶颈效应等. 这些小尺度体系的热输运性质可以很好地用非平衡格林函数来描述. 本文首先介绍了量子热输运的特性、声子非平衡格林函数方法及其在低维纳米材料中的研究进展; 其次回顾了近年来在 一系列低维材料中发现的热-自旋输运现象. 这些自旋热学现象展现了全新的热电转换机制, 有助于设计新型的热电转换器件, 同时也给出了用热产生自旋流的新途径; 最后介绍了线性响应理论以及在此理论框架下结合声子、电子非平衡格林函数方法进行的一些有益的探索. 量子热输运的研究对热效应基础研究以及声子学器件、能量转换器件的发展有着不可替代的重要作用.