  Recently many interesting magnetic nanostructures have been fabricated and
much attention is arising on the rich magnetic properties that originate in the
quantum effects eminent in the nanoscale world. One of the peculiar aspects of
the quantum effects is the spin excitation gap. In the spin-1/2 low-dimensional
systems, the spin gap often appears when the lattice dimerization or the
frustration in the spin-spin interaction are introduced. In the present study,
we investigate the ground-state property of the spin-1/2 antiferromagnetic spin
chiral nanotubes with the spatial modulation in the spin-spin interaction. The
ground-state phase diagrams of them are determined by observing the behavior of
the expectation value of the Lieb-Schultz-Mattis slow-twist operator calculated
by the quantum Monte Carlo method with the continuous-time loop algorithm. We
discuss the relation between the characteristic of the topology of the phase
diagram and the chiral vector of the nanotubes.
