Density matrix renormalization group study of critical behavior of thespin−12alternating Heisenberg chain

Abstract

We investigate the critical behavior of the $S=1/2$ alternating Heisenberg chain using the density matrix renormalization group. The ground-state energy per spin, ${e}_{0},$ and singlet-triplet energy gap $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\Delta}}$ are determined for a range of alternations $\ensuremath{\delta}.$ Our results for the approach of ${e}_{0}$ to the uniform chain limit are well described by $c{\ensuremath{\delta}}^{p},$ with $p\ensuremath{\approx}1.45.$ The singlet-triplet gap is also well described by a power law, with $p\ensuremath{\approx}0.73,$ 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 ${\ensuremath{\delta}}_{0}$ is present in the logarithms.