Quantum magnet offers a fascinating opportunity to explore novel phases of matter. One exemplary platform is quantum spin liquid (QSL), the massively entangled state whose fluctuating spins are disordered, which exhibits collective phenomena 'non-locality'. Its low-energy physics is described by the emergent gauge fields mediated by the fractionalized excitations in the language of lattice gauge theory. Our interests are searching universal properties of QSL, new phases descend from QSL, and the experimental predictions to identify the non-locality. In addition, we are also interested in exotic quantum materials where multipolar degrees of freedom play the role with anomalous characteristics. 

Our interest lies in finding new topological phases and their consequence in electronic and magnetic sytems. Along with recent experiments, we focus on . In addition, quasi-two dimensional van-der Waals materials including twisted bilayer graphene are explored in the aspect of emergent topological properties.

We are interested in systems that have quasi-periodicity either spatially or temporally. In such systems, the lack of unit length or time scale prohibits defining crystal momentum and dispersion relation. Instead, it gives unique physical phenomena such as the multi-fractal spectrum and states. We study such unique physical phenomena using abstract mathematical concepts of the tiling space (e.g. pattern equivariant topology, gap labeling theorem).

Non-equilibrium systems are gaining concentration due to their various dynamic properties. Some topics in non-equilibrium systems can be found also in equilibrium systems, such as topological numbers or spin transportation, and some are not, such as Floquet theory or charge pumping. By studying these topics, we expect to find out exotic properties of non-equilibrium systems, and suggest experiments to realize them.