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

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^-4 (in units of J) decisively rules out power-law behavior for any alternation {δ}>0.001 and is consistent with δ4/3/{}ln{δ}{} 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.