Spin-Peierls instability in the spin-1/2 transverse XX chain with Dzyaloshinskii-Moriya interaction

We calculate exactly the density of magnon states of the regularly alternating spin-1/2 XX chain with Dzyaloshinskii-Moriya interaction. The obtained results permit us to examine the stability of the chain with respect to spin-Peierls dimerization. We found that depending on the dependences of Dzyaloshinskii-Moriya interaction on distortion amplitude it may act either in favour of the dimerization or against the dimerization.