Wolf, Dietrich; Zittartz, Johannes:

On the one-dimensional spin-1/2-Chain and its related fermion model

In: Zeitschrift für Physik. B Condensed Matter, Jg. 43 (1981) ; Nr. 2, S. 173-183
ISSN: 0340-224X
Zeitschriftenaufsatz / Fach: Physik
We study the linear anisotropic spin-1/2-Heisenberg model with periodic as well as
antiperiodic boundary conditions. Using two assumptions about the eigenvalues of the
related fermion models it is shown, how the exactly known energy spectrum of the
periodic Heisenberg model is altered in the antiperiodic case. This investigation provides
the basis for a subsequent test of a Hartree-Fock approximation. It gives fairly
good results for the groundstate energy and the energy dispersion of low-lying excitations.
Hartree-Fock solutions with gapless excitations yield a qualitatively correct
picture of the phase diagram of the Heisenberg model.