The energy spectrum of a spin-1/2 ladder with mixed interactions

We studied the energy spectrum of two coupled XY spin-1/2 chains with diffe rent exchange integrals and inter-chain interaction of Ising type. The thor ough analytical treatment of two-magnon states was given for finite and inf inite lattice strips. To study the case of macroscopic number of inverted s pins we used the corresponding density matrix renormalization group (DMRG) simulation. We also derived the self-consistent Bardeen-Cooper-Schrieffer ( BCS) estimates for the lowest energies of the system. The comparison of the BCS and the DMRG estimates has shown incorrect behaviour of the BCS approx imation for energy as a function of the intra-chain exchange integrals. To use the analytical results for two-magnon bound states we proposed a simple approximate formula for the lowest n-magnon energies of an infinite ladder with a more correct dependence on model parameters.