Our group investigates fundamental problems in condensed matter physics through massively parallel computation using ISSP supercomputers and “K-computer” at Kobe. For this purpose, we also develop new algorithms. As for quantum critical phenomena, for example, we are trying to find a “deconfined” critical phenomena, a new category of quantum phase transition, as a transition between Neel state and VBS state in the SU(N) Heisenberg model. Another target in this area of research is the existence/absence of super-solid phase in optical lattices and in He4 systems adsorbed on graphite surfaces. As for classical systems, we investigate the phase transition due to the Z2 vortex dissociation, an unconventional critical phenomena caused by the symmetry-breaking dangerously-irrelevant field, etc. Our most recent activities are focused on developments of tensor network methods and their applications to frustrated spin systems.

A super-operator that defines renormalization transformation of two-site operators. Each tensor represented by a polygon is computed through MERA.

Scaling-dimensions obtained by solving the eigenvalue problem of the super-operator.

Clues and criteria for designing a Kitaev spin liquid revealed by thermal and spin excitations of the honeycomb iridate <math> <mrow> <msub> <mi>Na</mi> <mn>2</mn> </msub> <msub> <mi>IrO</mi> <mn>3</mn> </msub> </mrow> </math>: Y. Yamaji, T. Suzuki, T. Yamada, S.-I. Suga, N. Kawashima and M. Imada, Phys. Rev. B93 (2016) 174425.

Tensor network algorithm by coarse-graining tensor renormalization on finite periodic lattices: H.-H. Zhao, Z.-Y. Xie, T. Xiang and M. Imada, Phys. Rev. B93 (2016) 125115(1-14).

Quantum Spin Liquid in Spin 1/2 J_{1}–J_{2} Heisenberg Model on Square Lattice: Many-Variable Variational Monte Carlo Study Combined with Quantum-Number Projections: S. Morita, R. Kaneko and M. Imada, J. Phys. Soc. Jpn.84 (2015) 024720 (1-11).