  The interplay between frustration and quantum fluctuation in magnetic systems
is known to be the origin of many exotic states in condensed matter physics. In
this paper, we consider a frustrated four-leg spin tube under a magnetic field.
This system is a prototype to study the emergence of a nonmagnetic ground state
factorizable into local states and the associated order parameter without
quantum fluctuation, that appears in a wide variety of frustrated systems. The
one-dimensional nature of the system allows us to apply various techniques: a
path-integral formulation based on the notion of order by disorder,
strong-coupling analysis where magnetic excitations are gapped, and
density-matrix renormalization group. All methods point toward an interesting
property of the ground state in the magnetization plateaus, namely, a quantized
value of relative magnetizations between different sublattices (spin imbalance)
and an almost perfect factorization of the ground state.
