Variational studies of strongly-correlated systems

我的研究计划专注于开发精确的、但在计算上有效的变分近似，以回答在研究强关联系统中出现的关键问题，即如何预测：(I)当电荷载流子被声子、磁子、等离子激子等激发云“覆盖”时形成的准粒子的特征。在某些情况下，这种准粒子被称为极化子；(Ii)准粒子之间通过其云之间的激发交换而产生的有效相互作用的特征；以及(Iii)它们对宿主材料性质的综合影响。目前没有处理这类问题的一般理论框架，这阻碍了在确定技术用途的最佳材料方面取得进展。我们的长期目标是建立这样一个框架。 我们的工作是基于我们的独特方法，即识别对穿衣云结构做出贡献的最重要的真实空间构型，并保持它们对所有订单的贡献。我们证明，这导致了对单极化子和双极化子的非常准确的预测，即使是对于强耦合，这很难用其他方法来研究。在接下来的5年里，我们将进一步扩展我们方法的能力，并将其用于研究： 项目1：低载流子浓度系统中强载流子-玻色子耦合的影响； 项目2：在半填充和接近半填充的系统中的强载流子-玻色子耦合的影响； 项目3：有限温度下极化子的性质； 项目4：驱动系统中极化子的性质； 项目5：将我们的变分方法扩展到强关联电子哈密顿量。 我的研究计划从研究单极化子和双极化子到研究有限载流子浓度的系统的稳步进展表明，这个计划已经达到了一个成熟的阶段，它将产生突破性的影响：我们目前是世界上唯一能够准确和有效地解决项目1中包括的问题的小组：米格达尔定理在这里无效，数值模拟在非常低的密度下很难进行，因为它们需要考虑非常大的系统。我们也是目前唯一能够回答项目3的问题的小组。在这里，最先进的数值研究仅限于具有多达10个位置的链，而我们可以研究任何无限大的晶格。这些都是低风险、高回报的项目。相比之下，高风险、高回报的项目2、4和5专注于将我们的专业知识扩展到更广泛的相关问题类别。 所有这些项目都为本科生、研究生和博士后研究员提供了极好的培训，因为它们结合了磨练一个人的物理直觉(找到对云重要的配置)、分析能力(推导得出的方程式)、编程能力(编写解决方案)和演示技能。

My research program is focused on developing accurate, yet computationally efficient, variational approximations for answering the key questions that arise in the study of strongly correlated systems, i.e. how to predict: (i) the characteristics of the quasiparticle that forms when a charge carrier becomes "dressed'' by a cloud of excitations such as phonons, magnons, plasmons, etc. In certain cases, this quasiparticle is called a polaron; (ii) the characteristics of the effective interactions arising between quasiparticles through exchange of excitations between their clouds; and (iii) their combined influence on the properties of the host material. There is currently no general theoretical framework for dealing with such problems, hindering progress in identifying optimal materials for technological uses. Our long-term objective is to develop such a framework. Our work is based on our unique approach of identifying the most important real-space configurations that contribute to the structure of the dressing clouds, and keeping their contributions to all orders. We demonstrated that this leads to very accurate predictions for single polarons and bipolarons even for strong couplings, difficult to study by other means. In the next 5 years we will further expand the capabilities of our method, and use it to study: Project 1: the effects of strong carrier-boson coupling in systems with low carrier concentrations; Project 2: the effects of strong carrier-boson coupling in systems at and near half-filling; Project 3: properties of polarons at finite temperatures; Project 4: properties of polarons in driven systems; Project 5: extensions of our variational approach to strongly correlated electronic Hamiltonians. The steady progress of my research program from the study of single polarons and bipolarons, to the study of systems with finite carrier concentrations, shows that this program has reached a mature stage where it will have a ground-breaking impact: We are currently the only group in the world able to accurately and efficiently solve the problems included in Project 1: the Migdal theorem is not valid here and numerical simulations are difficult at very low densities as they require considering very large systems. We are also the only group currently able to answer the questions of Project 3. Here, state-of-the-art numerical studies are limited to chains with up to 10 sites, whereas we can study any infinite lattices. These are low-risk, high reward projects. In contrast, the high-risk, high reward Projects 2, 4 and 5 focus on expanding our expertise to an even wider class of relevant problems. All these project offer excellent training to undergraduate and graduate students and postdoctoral fellows, because they combine honing one's physical intuition (in finding the configurations important to the clouds), analytical abilities (deriving the resulting equations), programming abilities (coding the solution) and presentation skills.