Spin chains with long range RKKY interaction

Spin-chains are not well ordered antiferromagnets: their correlations decay algebraically and they do not develop true long-range order. Higher dimensional magnets may develop long-range order and, in such a case, the excitations are gapless magnons with well-defined Goldstone modes. To reconcile these two pictures we interpret magnons as bound states of spinons. The introduction of antiferromagnetic long-range RKKY interactions effectively increases the dimensionality of the chains and allow them to develop long range AFM order without violating Mermin-Wagner’s theorem. We study the transition from gapless disordered to gapless ordered phases through the spin dynamical structure factor with the DMRG method. We identify signatures of bound states leaking out from the spinon continuum and the formation of coherent Goldstone modes. We also consider the effects of easy-axis anisotropy and we compare to predictions from spin-wave theory.