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: $ 3.64万
• 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: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=657071
• 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.

***凝结物理学的主要目标之一是了解多体系统（例如固体）的集体行为。但是，通常很难在组成粒子之间存在相互作用的情况下预测其行为。在固体中，由于量子机械不确定性原理，电子之间的相互作用在零温度下也会在电子状态下产生波动。量子波动使基于经典概念的多体系统的行为很难描述，该概念认为粒子可以同时具有确定的位置和动量。用于研究相互作用的传统理论方法将相互作用视为添加到非相互作用系统中的小扰动。尽管扰动方法对于弱相互作用的系统效果很好，但对于强烈的交互系统而言，它巨大失败。缺乏能够描述密切相关的量子多体系统行为的一般理论工具一直是理论凝结物理学中最大的障碍之一。 ******强烈互动的效果在几乎没有能量的状态的系统中变得尤为重要。金属就是这样的例子。在金属中，由于其高电导率，电子的能量成本很小，因此可以轻松地改变其状态。传统金属的物理特性众所周知，这对于当前技术的开发至关重要。但是，在过去三十年中发现的许多新材料（例如高温超导体）无法使用应用于常规材料的相同技术来理解。这些非常规的金属通常在电子状态进行全局重排的量子相变近近期出现。近相转换，由于系统即将开发新的布置模式，因此存在强大的量子波动。在临界点，电子不再像动作那样独立的颗粒受到波动的强烈扰动。尽管强烈的理论努力致力于由于强烈的量子波动而产生的非常规的金属状态，但很难理解这种强烈相互作用金属的精确性质。****** **************的目的是了解集体行为在汇总的量子量强烈的量子中，例如，量子化的量子化量很大。特定项目包括开发能够包括强相关性影响并将方法应用于材料的新理论方法。 了解密切相关的材料会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南。