Spectral excitations in the one-dimensional spin-½ dimerized Heisenberg chain: A renormalization-group approach

Abstract

A zero-temperature lattice renormalization-group calculation is presented and applied to the antiferromagnetic one-dimensional dimerized spin-½ Heisenberg chain. The calculation indicates the existence of a gap in the spectrum of the dimer system, which vanishes only in the limit of a uniform spin chain. To improve the accuracy of the numerical estimates of the ground-state energy and gap, an iterative extension of finite-chain techniques is also applied. These approximate techniques are checked against the dimerized $\mathrm{XY}$ chain, for which an exact solution is found.