Field theoretic and holographic approaches to strongly correlated quantum many-body systems

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Condensed matters systems, that include metals and insulators, are made of many particles of the order of ten to the twenty three. Behaviors of individual particles are governed by the well established law of physics, quantum mechanics. It is straightforward to apply quantum mechanics to condensed matter systems if interactions between particles are weak. In weakly interacting systems, one can predict behaviors of a whole system by studying individual particles one by one because correlations between particles are weak. However, such `single-particle approaches' drastically fail when there are strong interactions and correlations between particles. This turns out to be the case in many recently discovered materials, such as high temperature superconductors. In those materials, one can not understand physical properties without understanding the system as a whole because behaviors of individual particles are strongly affected by other particles. It is generally impossible to solve those problems from first-principle calculations because there are so many degrees of freedom that are entangled with each other through strong interactions. On the other hand, strongly correlated systems often show new types of unexpected collective phenomena as a result of non-trivial quantum mechanical entanglements between particles. For example, electric current flows without any resistance even in the presence of impurities in superconducting state, and conductance is quantized independent of details of samples in quantum Hall states. When a condensed matter system shows distinct collective behaviors, it is a sign that the system is in a new phase of matter. My research is concerned about theoretically understanding novel collective phenomena that arise in strongly correlated quantum many-body systems. I focus on a small set of collective degrees of freedom in order to capture essential phenomena in an efficient way instead of trying to understand all the microscopic details in many-body systems. The present research will not only help us to improve our fundamental understanding of strongly correlated quantum many-body systems, but also to use various novel materials for applications, such as information technology.