Spin Nematic Phase of the Quantum Spin Nanotube

The S=1/2 three-leg quantum spin nanotube with the ring exchange interaction is investigated using the numerical exact diagonalization of finte-size clusters and finite-size scaling analysis. The previous study suggested that the ring exchange interaction induces the quantum phase transition from the spin gap phase to some new phase. The present work indicates that the new phase is the spin nematic Tomonaga-Luttinger liquid phase