INTERCHAIN-COUPLING EFFECT ON THE ONE-DIMENSIONAL SPIN-1/2 ANTIFERROMAGNETIC HEISENBERG-MODEL

Within a mean-field theory, the disordered spin-1/2 single-chain state is shown to be unstable towards an antiferromagnetically, long-range ordered one, when any finite transverse coupling, J(perpendicular-to), is introduced between chains. A mean-field Hamiltonian is derived from the Heisenberg model, using an extension of the Wigner-Jordan transformation in two dimensions. The staggered magnetization and the ground-state energy are calculated for values of transverse couplings ranging from 0 to 1. The main consequence of these calculations is that the value of J(perpendicular-to), required to have antiferromagnetic long-range order, must only be nonzero. This result is consistent with that of Sakai and Takahashi indicating that the critical transverse coupling should be of order of the inverse of the one-dimensional staggered magnetic susceptibility. Following a qualitative argument, it can also suggest that the Luttinger-liquid state is unstable at least at nearly half-filling for the Hubbard model in the limit of large Coulomb repulsion.