Non-perturbative studies of strongly correlated quantum many-body systems

强相关量子多体系统的非微扰研究

• 批准号: RGPIN-2018-05502
• 负责人: Lee, SungSik
• 金额: $ 7.29万
• 依托单位: McMaster University
• 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=763030
• 关键词: Non; perturbative; studies; strongly; correlated

One of the primary goals in condensed matter physics is to understand collective behaviours of many-body systems such as solids. However, it is generally difficult to predict their behaviours in the presence of interactions among constituent particles. In solids, interactions among electrons generate fluctuations in the electronic state even at zero temperature due to the quantum mechanical uncertainty principle. The quantum fluctuations make it hard to describe the behaviours of many-body systems based on the classical concept which posits that particles can have definite positions and momenta simultaneously. The traditional theoretical method that has been used to study the effect of interactions treats interactions as small perturbations added to non-interacting systems. While the perturbative approach works well for weakly interacting systems, it fails drastically for strongly interacting systems. The absence of a general theoretical tool that is capable of describing behaviours of strongly correlated quantum many-body systems has been one of the biggest obstacles in theoretical condensed matter physics. The effect of strong interactions becomes particularly important in systems whose states can be changed with little energy. Metals are one such example. In metals, electrons can easily change their states with little cost in energy due to their high conductivity. Physical properties of conventional metals are well understood, which was crucial for the development of current technology. However, many new materials such as high temperature superconductors that have been discovered over the past thirty years cannot be understood using the same techniques applied to conventional materials. These unconventional metals often arise near quantum phase transitions in which electronic states undergo a global rearrangement. Near phase transitions, there exist strong quantum fluctuations as systems are on the verge of developing new patterns of arrangement. At critical points, electrons no longer move as independent particles as their motions are strongly perturbed by the fluctuations. Despite the intense theoretical effort devoted to the unconventional metallic states that arise as a result of strong quantum fluctuations, it has been difficult to understand the precise nature of such strongly interacting metals.The goal of the proposed research is to understand collective behaviours that emerge as a result of strong interactions in condensed matter systems such as the unconventional metals realized near quantum phase transitions. The specific projects include developing new theoretical methods that are capable of including the effects of strong correlations, and applying the methods to materials. Understanding strongly correlated materials can impact future devices and applications, and provide an important guide in the search for new high-performance materials.

凝聚态物理学的主要目标之一是了解固体等多体系统的集体行为。然而，在组成粒子之间存在相互作用的情况下，通常很难预测它们的行为。在固体中，由于量子力学测不准原理，即使在零温度下，电子之间的相互作用也会产生电子态的涨落。量子涨落使得基于经典概念的多体系统的行为很难描述，经典概念假设粒子可以同时具有确定的位置和动量。用来研究相互作用影响的传统理论方法把相互作用看作是加在非相互作用系统上的微小扰动。虽然微扰方法对弱相互作用系统很有效，但对于强相互作用系统却严重失败。缺乏能够描述强关联量子多体系统行为的通用理论工具一直是理论凝聚态物理中的最大障碍之一。在状态可以用很少的能量改变的系统中，强相互作用的影响变得特别重要。金属就是这样一个例子。在金属中，由于其高导电性，电子可以很容易地改变它们的状态，而几乎不需要花费能量。人们很好地了解了传统金属的物理性质，这对当前技术的发展至关重要。然而，过去30年来发现的许多新材料，如高温超导体，不能用应用于传统材料的相同技术来理解。这些非常规金属经常出现在电子态经历全局重排的量子相变附近。在相变附近，由于系统即将发展出新的排列模式，存在着强烈的量子涨落。在临界点，电子不再作为独立的粒子运动，因为它们的运动受到涨落的强烈扰动。尽管人们对强量子涨落引起的非常规金属态进行了大量的理论研究，但很难理解这种强相互作用金属的确切性质。拟议研究的目标是理解凝聚态系统中由于强相互作用而出现的集体行为，例如在量子相变附近实现的非传统金属。具体项目包括开发能够包括强相关性影响的新理论方法，并将这些方法应用于材料。了解强关联材料可以影响未来的设备和应用，并为寻找新的高性能材料提供重要指导。