Nonperturbative methods for studying dressed quasiparticles and their effective interactions in strongly-coupled systems

一个电子在固体中的运动与它的所有基本激发（如晶格振动）密切相关，而且它在运动时会拖着沿着一团这种可能的激发。这种复杂的实体被称为“着装准粒子”。与原始电子相比，它具有不同的有效质量和动力学性质。修饰后的准粒子之间的相互作用也与原始电子之间的相互作用非常不同：它们的云之间的激发交换介导了一种有效的吸引力，可能导致超导性或其他有趣的行为。理解这些修饰准粒子的性质及其有效相互作用，以及它们对固体物理性质的综合影响，是推动理论凝聚态和材料物理学现代研究的基本问题。 在过去的十年里，我的研究计划一直专注于寻找高度准确但计算成本低廉的近似描述这样的准粒子和它们的相互作用在强耦合制度微扰方法失败。我的小组已经成功地开发了这样的方法的基础上变分原理和证明其准确性的比较与高精度的数值结果简单的模型，后者是可用的。我们还使用这些方法发现了某些类型的模型中非常意外的行为，这些模型以前没有被研究过，因为它们的复杂性使它们难以进行数值研究。 未来五年，我的主要目标是： a）使用我的小组已经开发的方法，提出和研究各种感兴趣的材料的实际有效模型，特别是那些属于所谓的“强相关”区域的材料。这些不能用微扰的方法来研究，数值研究通常局限于相当小的簇和/或高温，并且可能与感兴趣的物理学无关。这些材料包括铜酸盐、锰氧化物、铱酸盐、磷属元素化物，但也包括有机甚至生物系统，它们表现出丰富多样的性质，如高温超导性、巨磁阻、高温下的量子相干性等，仍然不为人所理解 B）将这些方法推广到有限浓度的粒子与各种类型的激发耦合的系统。这将使我们能够理解有效模型的准确性，这些模型正确地结合了准粒子的动力学及其有效相互作用，如在少粒子区域中计算的那样。这也将代表着在理解这些模型的性质方面的一个重大进步，这些模型与描述一些最迷人的材料有关，但对它们远离弱耦合状态的一般行为知之甚少。

An electron moving through a solid is intimately connected with all of its elementary excitations, such as lattice vibrations, and it drags along, as it moves, a cloud of such possible excitations. This complex entity is called a "dressed quasiparticle". Compared to the original electron, it has a different effective mass and dynamical properties. The interactions between dressed quasiparticles are also very different from those between the original electrons: exchange of excitations between their clouds mediates an effective attraction that may result in superconductivity or other interesting behavior. Understanding the nature of these dressed quasiparticles and their effective interactions, and their combined effect on the physical properties of the solid, are fundamental questions that drive a lot of the modern research in theoretical condensed matter and materials physics. Over the past decade, my research program has been focused on finding highly accurate yet computationally inexpensive approximations for describing such quasiparticles and their interactions in strongly coupled regimes where perturbative methods fail. My group has succeeded in developing such methods based on variational principles and proving their accuracy by comparison with highly accurate numerical results for simple models, where the latter are available. We have also used these methods to uncover very unexpected behavior in certain types of models that had not been investigated before because their complexity makes them difficult for numerical studies.  During the next five years, my main goals are: a) to use the methods already developed in my group to propose and study realistic effective models of various interesting materials, in particular those that fall in the so-called "strongly correlated" regime. These cannot be studied by perturbative means, and numerical studies are often restricted to rather small clusters and/or high temperatures, and may not be relevant for the physics of interest. Such materials, which include cuprates, manganites, iridates, pnictides, but also organic and even biological systems, exhibit a rich variety of properties like high-temperature superconductivity, colossal magnetoresistivity, quantum coherence at high temperatures, etc., that are still not understood.  b) to generalize these methods to systems with a finite concentrations of particles coupled to various types of excitations. This would allow us to understand how accurate are the effective models that correctly incorporate the quasiparticles' dynamics and their effective interactions, as calculated in the few-particle regime. It would also represent a significant advancement in understanding the properties of such models, which are relevant for describing some of the most fascinating materials and yet little is known about their generic behavior away from the weakly-coupled regime.