We investigate the critical behavior of the $S=1/2\mathrm{}$ alternating Heisenberg chain using the density matrix renormalization group. The ground-state energy per spin, $e_0,$ and singlet-triplet energy gap $\tilde{\Delta }$ are determined for a range of alternations $\delta .$ Our results for the approach of $e_0$ to the uniform chain limit are well described by $c{\delta }^p,$ with $p\approx \mathrm{1.45.}$ The singlet-triplet gap is also well described by a power law, with $p\approx 0.73,$ half of the $e_0$ power. The renormalization group predictions of power laws with logarithmic corrections can also accurately describe our data provided that a surprisingly large-scale parameter ${\delta }_0$ is present in the logarithms.

• Received 17 December 2002

DOI:https://doi.org/10.1103/PhysRevB.68.024416