Competition between singlet formation and magnetic ordering in one-dimensional spin systems

We study the behavior of a model of two XXZ spin chains coupled by an isotropic exchange interaction ${\mathit{J}}_{\mathit{K}}$ as the anisotropies and spin velocities in the individual chains are varied. In the limit of large antiferromagnetic ${\mathit{J}}_{\mathit{K}}$ we map the model’s low-energy sector onto an Ising model in a transverse field; in the limit of large ferromagnetic ${\mathit{J}}_{\mathit{K}}$ we map the model’s low-energy sector onto that of a single spin-one chain. For small ${\mathit{J}}_{\mathit{K}}$, we study the model perturbatively via Abelian and non-Abelian bosonization. We determine the possible phases, approximate locations of the phase boundaries, universality classes of the transitions, and asymptotic behavior of correlation functions. We believe our model captures the essential physics of the interplay between the compensation of local moments and magnetic ordering, which may be important for the heavy-fermion materials.