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

***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，由于量子力学不确定原理，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。量子涨落使得基于粒子可以同时具有确定位置和动量的经典概念来描述多体系统的行为变得困难。用于研究相互作用影响的传统理论方法将相互作用视为添加到非相互作用系统的小扰动。虽然扰动方法对于弱交互系统效果很好，但对于强交互系统却严重失败。缺乏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。 ******对于状态可以用很少的能量改变的系统来说，强相互作用的影响变得尤为重要。金属就是这样的例子之一。在金属中，由于其高导电性，电子可以轻松改变其状态，而几乎不需要消耗能量。传统金属的物理性质已被充分了解，这对于当前技术的发展至关重要。然而，过去三十年来发现的许多新材料，例如高温超导体，无法使用应用于传统材料的相同技术来理解。这些非常规金属通常出现在量子相变附近，其中电子态经历全局重排。在相变附近，由于系统即将发展出新的排列模式，因此存在强烈的量子涨落。在临界点，电子不再作为独立粒子运动，因为它们的运动受到波动的强烈扰动。尽管对强量子涨落产生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精确性质。******本研究的目标是了解凝聚态物质系统中强相互作用所出现的集体行为，例如在量子相变附近实现的非常规金属。具体项目包括开发能够包含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.