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

Abstract

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