Novel Phases of Quantum Matter

技术总结该奖项支持理论研究和教育，以探索强相互作用量子物质的性质，如在各种过渡金属化合物中实现的，以及在捕获的超冷原子系统中实现的。特别关注具有反铁磁性和高温超导性能的层状化合物：例如铜酸盐、磷酸盐化合物、贝克加德盐和稀土重费米子化合物。PI提出了一个通用相图，它成功地描述了这些综合系列材料的物理性质随温度、外加磁场和电子密度或压力等可调参数的变化。相图中的中心因素是金属和超导体中的量子相变，包括自旋磁性和其他顺序的开始。PI在两个空间维度上描述了这种跃迁理论的强耦合结构，并建议发展该理论以产生对我们理解的新的实验测试。该理论还允许出现更奇特的中间相，具有微妙的量子纠缠或“拓扑顺序”；PI将在与某些有机绝缘体的实验研究接触的同时研究它们的特征。强量子关联理论也将应用于捕获的超冷原子的实验，以及石墨烯中的电子自旋物理。最后，通过规范-引力二象性，在反德西特空间中，强相互作用量子物质的可能相和引力理论的状态之间也有显著的联系。该奖项还支持研究生和博士后水平的教育，以及对公众的推广和该领域下一版权威教科书的准备。非技术总结该奖项支持旨在探索量子物质的理论研究和教育。当大量相互作用的粒子在足够低的温度下形成量子物质时，量子力学的概念在确定其区别特征方面发挥了关键作用。对于固体中的电子来说，所需的“低温”温度甚至可能高于室温。对于被捕获的原子气体，需要从绝对零度开始大约十亿分之一度的超低温。值得注意的是，一套共同的想法已经在这种广泛的能源范围内得到了应用。量子物质中一些最有趣的阶段与磁性和超导电性之间的相互作用有关。电子可以被认为是微小的磁铁，而磁性是由电子磁轴的协同排列而产生的。超导性是电子对携带电流而不耗散的能力。PI将研究如何通过改变材料参数，将电子系统从磁性状态驱动到超导态，跨越各种“量子相变”。这种相变类似于常见的热转变，比如水变成水蒸气，但这里与电子之间微妙的量子关联有关。来自量子相变理论的概念有助于我们理解实验室中量子物质的可测量性质。PI还将探索量子物质理论与黑洞视界量子理论之间似乎无关的联系。这两个领域的共同兴趣是，有多少粒子可以在很长的距离内以量子力学的方式相互纠缠；它们对纠缠的不同方法带来了互惠互利的见解。该奖项还支持研究生和博士后水平的教育，以及对公众的宣传和该领域下一版权威教科书的准备。

TECHNICAL SUMMARYThis award supports theoretical research and education to explore the properties of strongly interacting quantum matter, as realized in a wide variety of transition metal compounds, and in systems of trapped ultra-cold atoms. Special attention will be paid to layered compounds with antiferromagnetism and higher temperature superconductivity: examples are the cuprates, the pnictide compounds, the Bechgaard salts, and rare-earth heavy-fermion compounds. The PI has proposed a common phase diagram which has successfully described the variation in physical properties as a function of temperature, applied magnetic field, and a tuning parameter like electron density or pressure, across these comprehensive series of materials. Central actors in this phase diagram are quantum phase transitions, involving the onset of spin magnetism and other orders, in metals and superconductors. The PI has described the strong-coupling structure of the theory of such transitions in two spatial dimensions, and proposed to develop the theory to produce new experimental tests of our understanding. The theory also allows for more exotic intermediate phases, with subtle types of quantum entanglement or 'topological order;' the PI will study their features while making contact with experimental studies on certain organic insulators. The theories of strong quantum correlations will also be applied to experiments on trapped ultra-cold atoms, and to electron spin physics in graphene. Finally, there are also remarkable connections between the possible phases of strongly interacting quantum matter, and the states of gravitational theories in anti-de Sitter space, through a gauge-gravity duality. The PI will continue his research at this interface area.This award also supports education at the graduate and postdoctoral level, as well as outreach to the public and the preparation of the next edition of an authoritative textbook in the field. NONTECHNICAL SUMMARYThis award supports theoretical research and education with the aim to explore quantum matter. Quantum matter is formed when large numbers of interacting particles are at temperatures low enough so that the concepts of quantum mechanics play a crucial role in determining its distinguishing characteristics. For electrons in solids, the needed 'low' temperatures can be even higher than room temperature. For gases of trapped atoms, ultra-cold temperatures about one billionth of a degree from the absolute zero of temperature are needed. Remarkably, a common set of ideas has found application across this wide range of energy scales. Some of the most interesting phases of quantum matter are associated with the interplay between magnetism and superconductivity. Electrons may be thought of as tiny magnets and magnetism arises from the co-operative arrangement of the magnetic axes of the electrons. Superconductivity is the ability of pairs of electrons to carry electrical current without dissipation. The PI will study how by varying material parameters, it is possible to drive a system of electrons from a magnetic to a superconducting state, across a variety of 'quantum phase transitions.' Such phase transitions are analogous to familiar thermal transitions, like water changing to steam, but are associated here with subtle quantum correlations between the electrons. Concepts from the theory of quantum phase transitions inform our understanding of the measureable properties of quantum matter in the laboratory.The PI will also explore emerging connections between the theory of quantum matter, and seemingly unrelated work on the quantum theory of black hole horizons. These fields share a common interest in how many particles can become 'entangled' with each other quantum mechanically across large distances; their distinct approaches to entanglement have led to mutually beneficial insights.This award also supports education at the graduate and postdoctoral level, as well as outreach to the public and the preparation of the next edition of an authoritative textbook in the field.