Variational studies of strongly-correlated systems

强相关系统的变分研究

• 批准号: RGPIN-2020-04634
• 负责人: Berciu, Mona
• 金额: $ 3.64万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=762930
• 关键词: Variational; studies; strongly; correlated; systems

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.

我的研究计划的重点是开发准确但有效的变化近似，以回答对密切相关的系统的研究中出现的关键问题，即如何预测：（i）当电荷携带者被诸如诸如phormons，pollaston，polor ii confone of polor的云的云云中时，载电携带者变得“打扮”时形成的quasiparticle的特征在云之间交换兴奋性的有效相互作用；（iii）它们对宿主材料的特性的综合影响，目前没有一般的理论框架来处理此类问题，从而阻碍了我们的长期范围的最佳构建方法。云，并保留对所有订单的贡献。我们证明，这也导致对单个极性子和双圆龙的非常准确的预测，即使对于强耦合，也很难通过其他方式研究。在接下来的5年中，我们将进一步扩展方法的能力，并使用它来研究：项目1：强载驾驶机耦合在载体浓度较低的系统中的影响；项目2：强载玻璃耦合在系统及半填充的系统中的影响；项目3：极性温度下极地的性质；项目4：极性在驱动系统中的特性；项目5：我们的变异方法的扩展，以强烈相关的电子哈密顿量。我的研究计划从单个极性和双极的研究到具有有限载体浓度的系统的稳定进步表明，该计划已达到一个成熟的阶段，它将产生突破性的影响：我们目前是世界上唯一能够准确有效地解决项目1中的问题：Migdal Theorem在这里很难考虑，并且很难考虑到很难的模拟，因为他们很难被认为是很难的，因为他们很难被划分。我们也是目前唯一能够回答项目3的问题的小组。在这里，最新的数值研究仅限于最多10个站点的链条，而我们可以研究任何无限晶格。这些是低风险，高奖励项目。相比之下，高风险，高奖励项目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。所有这些项目都为本科生和研究生和博士后研究员提供了出色的培训，因为它们结合了磨练自己的身体直觉（发现对云至关重要的配置），分析能力（得出结果方程），编程能力（编码解决方案）和介绍能力。