Our main focus is quantum many-body theory. Based on the close correspondence among quantum many-body systems, classical statistical systems, and field theory, we pursue universal concepts in physics. As an example of our recent achievements, based on anomaly in quantum field theory, we introduced a new classification of gapless quantum critical phases in the presence of symmetries. This opened up a new direction in classification of quantum phases. Taking advantage of novel theoretical concepts, we also aim to give a unified picture on experimental data and to make testable predictions for experiments. For example, recently we introduced a “network model” of quantum wires in order to describe electronic states in the charge-density-wave material 1T-TaS₂ and demonstrated a realization of flat bands. Unlike most of the other constructions of flat bands, the flatness is protected by symmetries and is robust. The network model will be a new platform to realize many interesting phenomena including superconductivity and non-Fermi liquids. Much of our research is carried out in international collaborations.

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