  We study the ground state phase diagram of a frustrated spin-1/2 four-leg
spin tube in an external magnetic field. We explore the parameter space of this
model in the regime of all-antiferromagnetic exchange couplings by means of
three different approaches: analysis of low-energy effective Hamiltonian (LEH),
a Hartree variational approach (HVA) and density matrix renormalization group
(DMRG) for finite clusters. We find that in the limit of weakly interacting
plaquettes, low-energy singlet, triplet and quintuplet states play an important
role in the formation of fractional magnetization plateaux. We study the
transition regions numerically and analytically, and find that they are
described, at first order in a strong- coupling expansion, by an XXZ spin-1/2
chain in a magnetic field; the second-order terms give corrections to the XXZ
model. All techniques provide consistent results which allow us to predict the
existence of fractional plateaux in an important region in the space of
parameters of the model.
