Recent experiments have revealed the role of staggered Dzialoshinskii-Moriya interaction in the magnetized phase of an antiferromagnetic spin 1/2 two-leg ladder compound under a uniform magnetic field. We derive a low energy effective field theory describing a magnetized two-leg ladder with a weak staggered Dzialoshinskii-Moriya interaction. This theory predicts the persistence of the spin gap in the magnetized phase, in contrast to standard two-leg ladders, and the presence of bound states in the excitation spectrum. Such bound states are observable in Raman scattering measurements. These results are then extended to intermediate Dzialoshinskii-Moriya interaction using Exact Diagonalizations.
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