Ground-state alternation and excitation energy of S=(1/2) linear Heisenberg antiferromagnets

Abstract

The ground-state energy per site, \ensuremath{\epsilon}(\ensuremath{\delta}), and the singlet-triplet gap, \ensuremath{\Delta}(\ensuremath{\delta}), of the linear spin-(1/2) alternating Heisenberg antiferromagnet are found by extrapolation of direct solutions to N\ensuremath{\le}26 sites for even rings and N\ensuremath{\le}21 sites for odd rings, whose orbital degeneracy leads to qualitatively different critical behavior. The \ensuremath{\epsilon}(\ensuremath{\delta}) accuracy of ${<10}^{\mathrm{\ensuremath{-}}4}$ (in units of J) decisively rules out power-law behavior for any alternation \ensuremath{\delta}>0.001 and is consistent with ${\ensuremath{\delta}}^{4/3}$/\ensuremath{\Vert}ln\ensuremath{\delta}\ensuremath{\Vert} for \ensuremath{\delta}<0.05. The gap \ensuremath{\Delta}(\ensuremath{\delta}) is slightly sublinear in \ensuremath{\delta}. Direct ground-state solutions are found via diagrammatic valence-bond methods and provide sensitive tests for theoretical approaches to linear spin systems.