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

一个穿过固体的电子与它的所有基本激发密切相关，例如晶格振动，当它移动时，它拖着一团这样可能的激发云。这种复杂的实体被称为“修饰过的准粒子”。与原始电子相比，它具有不同的有效质量和动力学性质。经过修饰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调解了一种有效的吸引，这可能导致超导或其他有趣的行为。了解这些被修饰的准粒子的性质和它们的有效相互作用，以及它们对固体物理性质的综合影响，是推动许多现代理论凝聚态和材料物理研究的基本问题。 在过去的十年里，我的研究计划一直专注于寻找高精度但计算成本低的近似来描述这种准粒子及其在强耦合区域中的相互作用，在这些区域，微扰方法是无效的。我的团队已经成功地开发了基于变分原理的这种方法，并通过与简单模型的高精度数值结果进行比较来证明它们的准确性，后者是可用的。我们还使用这些方法在某些类型的模型中发现了非常意想不到的行为，这些类型的模型以前没有被研究过，因为它们的复杂性使得它们很难进行数值研究。 今后五年，我的主要奋斗目标是： A)使用我的小组已经开发的方法，提出和研究各种有趣材料的现实有效模型，特别是那些属于所谓的“强相关”制度的材料。这些不能用微扰方法来研究，数值研究通常局限于相当小的星系团和/或高温，可能与感兴趣的物理无关。这类材料不仅包括铜酸盐、锰氧化物、虹彩、磷灰石，还包括有机甚至生物体系，表现出丰富的各种性质，如高温超导、巨磁阻性、高温下的量子相干等，这些性质尚不清楚。 B)将这些方法推广到具有有限浓度的粒子与各种类型的激励相耦合的系统。这将使我们了解正确地包含准粒子动力学及其有效相互作用的有效模型的精确度有多高，正如在少粒子区域中计算的那样。这也将代表着在理解这类模型的性质方面的重大进步，这些模型与描述一些最吸引人的材料有关，但人们对它们离开弱耦合体系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.