Quantum Phase Transition of the Twisted Spin Tube

The $S=1\mathrm{/}2$ twisted three-leg spin tube with the lattice distortion from the regular triangle to the isosceles one is investigated using the numerical diagonalization of finite-size clusters and the phenomenological renormalization group analysis. It is found that the quantum phase transition occurs from the spin gap phase to another one with respect to this lattice distortion.