Energy gap of spin nanotube

Recently some quantum spin systems on tube lattices, so-called spin nanotubes, have been synthesized. They are expected to be interesting low-dimensional systems like the carbon nanotubes. As a first step of theoretical study on the spin nanotube, we investigate the S=12 three-leg spin tube, which is the simplest one, using numerical analyses of finite clusters and a finite-size scaling technique. The spin gap, which is one of the most interesting quantities reflecting the macroscopic quantum effect, was revealed to be open for any finite rung exchange couplings, in contrast to the three-leg spin ladder system which is gapless. We also found a quantum phase transition caused by an asymmetric rung interaction. When one of the three rung coupling constants is changed, the spin gap vanishes very rapidly.