Spin - 1 2 Periodic Nonuniform Xx Chains and the Spin - Peierls Instability

Since the discovery of the inorganic spin-Peierls compound CuGeO3 the interest in the properties of spin-Peierls systems considerably increased [1]. The models that can be examined exactly play an important role in clarifying the generic features of such systems. An example of such a model is the spin1 2 XX chain that was studied in several papers [2, 3, 4] (note, however, that in the nonadiabatic limit such a spin chain does not permit exact analysis [5]). The aim of the present study is to examine the influence of an additional DzyaloshinskiiMoriya coupling on the spin-Peierls dimerization. The presence of such a term for CuGeO3 was proposed in [6, 7]. The multisublattice spin1 2 XX chain with the Dzyaloshinskii-Moriya interaction was introduced in [8]. In our study we follow the idea of [2] and compare the total ground state energy of the dimerized and uniform chains. However, in contrast to previous works [2, 3, 4, 8] we use the continued-fraction representation for the one-fermion Green functions [9] that allows a natural extension of the calculations for more complicated lattice distortions having finite period. We consider N → ∞ spins 12 on a circle with the Hamiltonian