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

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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.