Exact solution of an S=1/2 Heisenberg antiferromagnetic chain with long-ranged interactions

Abstract

The S=1/2 Heisenberg Hamiltonian H=1/2${\mathcal{J}}_{\mathrm{n}=1}^{\mathrm{N}\mathrm{\ensuremath{-}}1}$${\mathcal{J}}_{\mathit{m}=1}^{\mathit{N}}$${\mathit{J}}_{\mathit{n}}$${\mathrm{\ensuremath{\sigma}}}_{\mathit{m}}$\ensuremath{\cdot} ${\mathrm{\ensuremath{\sigma}}}_{\mathit{m}+\mathit{n}}$, with ${J}_{n}$=${J}_{0}$/${\mathrm{sin}}^{2}$(n\ensuremath{\pi}/N), is shown to have a simple singlet ground state in the form of a Jastrow function. The spectrum and correlations are explicitly known and the magnetic susceptibility is shown to be Pauli type at T=0. The model has a striking similarity to the nearest-neighbor isotropic Heisenberg model and may be viewed as a discretized version of the Sutherland-Calogero-Moser system.