Topological aspects of the quantum spin nanotube

The spin nanotube has attracted a lot of interest as an intersection between the strongly correlated electronics and the nanoscience. Among spin nanotubes we focus on the S = 1/2 three-leg spin tube, because it has the largest quantum fluctuation and the strongest frustration. Using the numerical exact diagonalization of the finite-cluster Heisenberg model, we reveal that two singlet ground states are degenerated in the spin gap phase of the spin tube. It is also found that the spin gap is characterized by the quantized Berry phase.