An overview of an exotic type of liquid Materials with interacting quantum spins that nevertheless do not order magnetically down to the lowest temperatures are candidates for a materials class called quantum spin liquids (QSLs). QSLs are characterized by long-range quantum entanglement and are tricky to study theoretically; an even more difficult task is to experimentally prove that a material is a QSL. Broholm et al. take a broad view of the state of the field and comment on the upcoming challenges. Science, this issue p. eaay0668 BACKGROUND Years ago, Lev Landau taught us how to think about distinct phases of matter through an order parameter that characterizes the symmetry-broken state relative to the symmetry-preserving state from which it emerges. More recently, however, it has been realized that not all phases of matter are captured by this paradigm. This was spectacularly demonstrated by the discovery of fractional quantum Hall states in the 1980s. Over the years, it has been elucidated that these states, along with their exotic excitations—quasiparticles carrying a rational fraction of the elementary charge of an electron—are the consequence of topological properties of ground state wave functions with a special type of long-range quantum entanglement. One might wonder whether analogous phenomena occur for spins. Whether these “quantum spin liquids” actually exist in nature has been the subject of much investigation. ADVANCES Since Philip Anderson contemplated the idea of quantum spin liquids in 1973, there has been a lot of research to establish what they are and how they can be characterized. Of particular note was the realization that an effective low-energy theory inevitably resembles the gauge theory treatments also invoked in high-energy physics. However, these gauge fields are “emergent” in the sense that they reflect important structure of the many-particle state. Specifically, they describe excitations that carry a fraction of the quantum of spin in terms of emergent quasiparticles with gauge charge and/or gauge flux, analogous to the electric charge and magnetic flux in electrodynamics. One consequence is that these quasiparticle excitations can have nontrivial statistical interactions when they are braided around each other. Although most studies have focused on gapped spin liquids, equally intriguing are gapless versions—for instance, ones where the quasiparticle (“spinon”) spectrum is that of relativistic electrons described by the Dirac equation. Much work has been done to address specific models and connect them to experimental analogs. This has involved a combination of analytically solvable models, as well as the development of new numerical methods that provide approximate solutions given a microscopic (lattice scale) Hamiltonian. Perhaps most excitingly, there has been an increasingly promising effort to identify quantum spin liquids in nature. Much of the work has focused on materials where the magnetic ions reside on lattices that frustrate classical magnetic order. Examples include the triangular, kagome, hyperkagome, and pyrochlore lattices. Several candidate materials have been discovered, including organic salts, where molecular dimers realize spin-½ degrees of freedom on a distorted triangular lattice; herbertsmithite, where spin-½ copper ions form a kagome lattice; and α-RuCl3, where j =1/2 ruthenium ions form a honeycomb lattice and that is thought to be proximate to the famous Kitaev model. All of these materials have properties reminiscent of spin liquids, though their documented fidelity as model systems is limited by disorder, subleading interactions, or lack of experimental information. OUTLOOK Given the infinite variety of potential materials and the many research groups now exploring this space, we are optimistic that a pristine materials realization of a quantum spin liquid will be discovered in the coming years. Perhaps even now a spin liquid exists in a long-forgotten drawer of a museum. Efforts to achieve ultrahigh-quality samples and new experiments designed to determine whether fractionalization and long-range entanglement occur in such materials will be key. In addition to tantalizing clues based on such techniques as thermal Hall conductivity, nuclear magnetic resonance, and inelastic neutron scattering, future methods may involve looking for spin currents to prove fractionalization, as has been done for charge degrees of freedom in the fractional quantum Hall case, or probing the range and character of quantum entanglement, as previously done in ultracold gases. Moreover, if quasiparticle excitations can be isolated and then manipulated, the prospect of a new form of topologically protected quantum computation also exists. Finally, chemically doped versions of spin liquids have been predicted to provide an unconventional route to superconductivity. The search for such phases will undoubtedly be an exciting undertaking. Emergent gauge theory as fluctuating loops. The loops are flux lines, with “particles” living at the ends of open lines. Left: The loops are dilute and small. The line connecting the particles costs a finite energy per unit length; the particles are confined. Right: The loops are numerous and include a fraction that are of macroscopic extent; the particles are free to move apart. This is the deconfined (spin liquid) phase. Spin liquids are quantum phases of matter with a variety of unusual features arising from their topological character, including “fractionalization”—elementary excitations that behave as fractions of an electron. Although there is not yet universally accepted experimental evidence that establishes that any single material has a spin liquid ground state, in the past few years a number of materials have been shown to exhibit distinctive properties that are expected of a quantum spin liquid. Here, we review theoretical and experimental progress in this area.

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量子自旋液体

具有相互作用的量子自旋但不会磁性排序到最低温度的奇异类型液体材料的概述是称为量子自旋液体 (QSL) 的材料类别的候选材料。QSL 的特点是长程量子纠缠，理论上研究起来很棘手；更困难的任务是通过实验证明材料是 QSL。布罗霍尔姆等人。广泛地看待该领域的状况，并对即将到来的挑战发表评论。科学，这个问题 p。eaay0668 背景 多年前，Lev Landau 教我们如何通过一个有序参数来思考物质的不同阶段，该参数描述了相对于对称破坏状态相对于它出现的对称保持状态的特征。然而，最近，人们已经意识到，并非物质的所有阶段都被这种范式所捕获。1980 年代分数量子霍尔态的发现有力地证明了这一点。多年来，人们已经阐明，这些状态及其奇异的激发（携带电子基本电荷的合理部分的准粒子）是基态波函数拓扑性质的结果，具有特殊类型的长程量子纠缠。人们可能想知道自旋是否会发生类似的现象。这些“量子自旋液体”是否真的存在于自然界一直是许多研究的主题。进展自从 1973 年菲利普·安德森考虑量子自旋液体的想法以来，已经进行了大量研究来确定它们是什么以及如何表征它们。特别值得注意的是，有效的低能理论不可避免地类似于高能物理学中也引用的规范理论处理方法。然而，这些规范场是“涌现”的，因为它们反映了多粒子态的重要结构。具体而言，他们根据具有规范电荷和/或规范通量的涌现准粒子描述了携带一部分自旋量子的激发，类似于电动力学中的电荷和磁通量。一个结果是，当这些准粒子激发相互交织在一起时，它们可能会产生非平凡的统计相互作用。尽管大多数研究都集中在有间隙的自旋液体上，但同样有趣的是无间隙版本——例如，准粒子（“自旋子”）光谱是狄拉克方程描述的相对论电子的光谱。已经做了很多工作来解决特定模型并将它们连接到实验类似物。这涉及到分析可解模型的组合，以及新数值方法的开发，这些方法提供给定微观（晶格尺度）哈密顿量的近似解。也许最令人兴奋的是，在自然界中识别量子自旋液体的努力越来越有希望。大部分工作都集中在磁性离子驻留在晶格上的材料上，这些材料破坏了经典的磁序。示例包括三角形、kagome、hyperkagome 和烧绿石晶格。已经发现了几种候选材料，包括有机盐、其中分子二聚体在扭曲的三角形晶格上实现了自旋 1/2 自由度；Herbertsmithite，其中自旋 ½ 铜离子形成 Kagome 晶格；和 α-RuCl3，其中 j =1/2 钌离子形成蜂窝晶格，这被认为与著名的 Kitaev 模型很接近。所有这些材料都具有让人联想到自旋液体的特性，尽管它们作为模型系统的记录保真度受到无序、次级相互作用或缺乏实验信息的限制。展望 鉴于潜在材料的多样性和目前正在探索这一领域的许多研究小组，我们乐观地认为，未来几年将发现量子自旋液体的原始材料实现。也许即使是现在，博物馆的一个被遗忘已久的抽屉里也存在一种旋转液体。实现超高品质样品的努力和旨在确定此类材料中是否发生分馏和长程纠缠的新实验将是关键。除了基于热霍尔电导率、核磁共振和非弹性中子散射等技术的诱人线索外，未来的方法可能涉及寻找自旋电流来证明分数化，就像分数量子霍尔情况下的电荷自由度所做的那样，或探索量子纠缠的范围和特征，就像之前在超冷气体中所做的那样。此外，如果准粒子激发可以被隔离然后被操纵，那么拓扑保护量子计算的新形式的前景也存在。最后，化学掺杂的自旋液体已被预测为超导提供了一种非常规的途径。寻找这些阶段无疑将是一项激动人心的事业。作为波动回路的涌现规范理论。环路是通量线，“粒子”位于开放线的末端。左：循环稀释且小。连接粒子的线每单位长度消耗有限的能量；粒子被限制。右：循环很多，包括宏观范围的一小部分；粒子可以自由移动。这是去限制（自旋液体）阶段。自旋液体是物质的量子相，具有由其拓扑特征产生的各种不同寻常的特征，包括“分馏”——表现为电子分数的基本激发。尽管还没有普遍接受的实验证据证明任何单一材料都具有自旋液体基态，但在过去几年中，许多材料已显示出量子自旋液体所期望的独特特性。在这里，我们回顾了该领域的理论和实验进展。