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. At the same time, we aim to give a unified picture on experimental data and to make testable predictions. As an example of our recent achievements, we have given a certain theoretical result for the total orbital angular momentum of chiral superfluids, which has remained paradoxical for 40 years. We also demonstrated, based on anomaly in quantum field theory, a new classification of gapless quantum critical phases in the presence of a discrete symmetry. This opens up a new direction in classification of quantum phases. In order to connect these theoretical developments with experiments, we also study material design to realize exotic topological phases such as Kitaev spin liquids. Much of our research is carried out in international collaborations.

Designing Kitaev spin liquid using Metal-Organic Framework (MOF). Kitaev model is an intriguing exactly solvable spin model, with a spin-liquid ground state. Although realizations of the Kitaev model in iridates and other inorganic materials has been discussed, the dominance of Heisenberg type interactions owing to direct exchanges prevents the ground state from becoming the spin liquid. We proposed a possibility of more ideal realizations of the Kitaev model, using MOFs in which direct exchange interactions are suppressed.

^{†}Stable Flatbands, Topology, and Superconductivity of Magic Honeycomb Networks: J. M. Lee, C. Geng, J. W. Park, M. Oshikawa, S.-S. Lee, H. W. Yeom and G. Y. Cho, Phys. Rev. Lett.124 (2020) 137002.

2.

Searching for an emergent SU(4) symmetry in real materials: M. Yamada, Department of Physics, Graduate School of Science, The University of Tokyo (2020).

Generalized Boundary Condition Applied to Lieb-Schultz-Mattis-Type Ingappabilities and Many-Body Chern Numbers: Y. Yao and M. Oshikawa, Phys. Rev. X10 (2020) 031008.

^{†}Refined symmetry indicators for topological superconductors in all space groups: S. Ono, H. C. Po and H. Watanabe, Sci. Adv.6 (2020) eaaz8367 (1-14).

^{†}Filling-enforced constraint on the quantized Hall conductivity on a periodic lattice: Y.-M. Lu, Y. Ran and M. Oshikawa, Annals of Physics413 (2020) 168060.