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

凝聚态物理的主要目标之一是理解多体系统（如固体）的集体行为。然而，通常很难预测它们在组成粒子之间存在相互作用时的行为。在固体中，由于量子力学的不确定性原理，即使在零温度下，电子之间的相互作用也会产生电子态的波动。量子涨落使得基于假设粒子可以同时具有确定的位置和动量的经典概念来描述多体系统的行为变得困难。研究相互作用效应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。虽然微扰方法对弱相互作用系统很有效，但对强相互作用系统却完全失效。缺乏一种能够描述强相关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的最大障碍之一。******强相互作用的影响在状态可以用很少的能量改变的系统中变得特别重要。金属就是这样一个例子。在金属中，由于电子的高导电性，电子可以很容易地以很少的能量成本改变它们的状态。人们对传统金属的物理性质有了很好的了解，这对当前技术的发展至关重要。然而，许多新材料，如在过去三十年中发现的高温超导体，不能用与传统材料相同的技术来理解。这些非常规金属通常出现在量子相变附近，在量子相变中，电子态经历了全局重排。在相变附近，当系统处于发展新的排列模式的边缘时，存在很强的量子涨落。在临界点上，电子不再像独立粒子那样运动，因为它们的运动受到涨落的强烈干扰。尽管人们在理论上付出了巨大的努力，致力于研究由于强量子涨落而产生的非常规金属态，但很难理解这种强相互作用金属的确切性质。******提出的研究目标是了解由于凝聚态物质系统（如实现近量子相变的非常规金属）中强相互作用而出现的集体行为。具体项目包括开发新的理论方法，能够包括强相关性的影响，并将这些方法应用于材料。了解强相关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。

***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.