Disorder and quantum criticality in itinerant antiferromagnets

总体目标是建立一个考虑所有软模的临界涨落和杂质和缺陷引起的失序的量子临界点附近的动态激发和输运理论。最近发现的铁基高温超导体以及对金属间重电子系统和过渡金属氧化物的研究表明，需要建立一个理论框架来解释接近临界的流动反铁磁体中的无序。在这些系统中，重要的是同时分析无序对集体序参量自由度和对费米能量附近电子的影响。与绝缘的量子磁体相比，受无间隙电子激发控制的金属产生了新的临界行为。除了正式开发新的理论框架外，我们的项目还将与上述材料中的实验进行详细的比较。在失序消失的极限下，理论应恢复波动自旋密度波的分析结果。在电子-电子相互作用消失的极限下，该理论将恢复无序电子的已知行为，包括弱和强局域化。开发这样一个理论是重要的原因:我),它使我们能够判断的部分或全部观测难题社区可以合理化是由于临界的微妙的相互影响和障碍,2)实验一些系统似乎同意传统的理论和我们的工作将明确预测对于物理障碍引起的小说,和iii)的理论,我们提出发展承诺构成小说关键行为。我们计划建立一个控制良好的理论，对金属在反铁磁量子相变附近的热力学、光谱和输运性质做出稳健可靠的预测。然后，我们将开发一种受控计算，其中在相同的基础上处理临界波动和无序。该理论的小参数是1/N，其中N是费米子口味（波段）的数量。这种扩展允许研究强无序和大自旋-电子耦合的极限。它成功地用于解决没有相互作用的无序问题，并包括强无序或二维系统中的局部化物理。它也被用于清洁量子临界系统，在那里它导致非费米液体的行为。我们还将讨论统计上罕见的区域和液滴的作用，这些区域和液滴会导致量子格里菲斯行为、激活的缩放和相变的涂抹。

The overall goal is to develop a theory for dynamic excitations and transport near a quantum critical point that takes into account critical fluctuations of all soft modes and disorder due to impurities and imperfections. The recently discovered iron-based high-temperature superconductors as well as investigations of inter-metallic heavy-electron systems and transition-metal oxides demonstrate the need to establish a theoretical framework that accounts for disorder in itinerant antiferromagnets close to criticality. In these systems it is important to analyze simultaneously the impact of disorder on the collective order-parameter degrees of freedom and on the electrons near the Fermi energy. Metals, being governed by gapless electronic excitations, give rise to new critical behavior compared to insulating quantum magnets. In addition to the formal development of a new theoretical framework, our project will be concerned with a detailed comparison with experiments in the mentioned materials. In the limit of vanishing disorder the theory should recover the results obtained from the analysis of fluctuating spin density waves. In the limit of vanishing electron-electron interactions the theory will recover the known behavior of disordered electrons, including weak and strong localization. To develop such a theory is important for a number of reasons: i) it enables us to judge whether some or all of the observations that puzzle the community can be rationalized as being due to the subtle interplay of criticality and disorder, ii) experiments in some systems seem to agree with the conventional theory and our work will make clear predictions with regards to disorder induced novel physics, and iii) the theory that we propose to develop promises to constitute novel critical behavior.We plan to formulate a well-controlled theory to make robust and reliable predictions for thermodynamic, spectroscopic and transport properties of metals near antiferromagnetic quantum phase transitions. We will then develop a controlled calculation where critical fluctuations and disorder are treated on the same footing. The small parameter of the theory is 1/N, where N is the number of fermion flavors (bands). This expansion allows the investigation of the limit of strong disorder and large spin-electron coupling. It was successfully used to solve disordered problems without interactions and includes the physics of localization in strongly disordered or two dimensional systems. It was also used in clean quantum critical systems, where it leads to non-Fermi liquid behavior. We will also address the role of statistically rare regions and droplets that lead to quantum Griffith behavior, activated scaling and smearing of the phase transition.