Vector chirality and inhomogeneous magnetization in frustrated spin   tubes in high magnetic fields
  The low-energy physics of three-leg frustrated antiferromagnetic spin-S tubes in the vicinity of the upper critical field are studied. Utilizing the effective field theory based on the spin-wave approximation, we argue that in the intermediate-interchain-coupling regime, the ground state exhibits a vector chiral order or an inhomogeneous magnetization for the interchain (rung) direction and the low-energy excitations are described by a one-component Tomonaga-Luttinger liquid (TLL). In both chiral and inhomogeneous phases, the Z_2 parity symmetry along the rung direction is spontaneously broken. It is also predicted that a two-component TLL appears and all the symmetries are restored in the strong-rung-coupling case. 
Masahiro Sato and Toru Sakai