Magnetization Curve at Zero Temperature for the Antiferromagnetic Heisenberg Linear Chain

The highest and lowest energies as a function of the total spin are computed for the class of "unbound" states in the Bethe formalism for the linear chain of spin-½ atoms with a Heisenberg exchange interaction between nearest neighbors. The lowest energies are used to compute the magnetization curve for the infinite antiferromagnetic chain in the limit of zero temperature. At zero temperature and in zero field, the magnetic susceptibility has the value 0.050661 $\frac{g^2{\mu }^2}{J}$, where $\mu$ is the Bohr magneton, $g$ the electron $g$ factor, and the interaction between neighboring spins is of the form $2J{\mathbf{S}}_1·{\mathbf{S}}_2$.