Renormalization group and other calculations for the one-dimensional spin-1/2 dimerized Heisenberg antiferromagnet

Publisher Website
Google Scholar
Abstract
A zero‐temperature renormalization group (RG) approach is applied to the one‐dimensional, spin‐1/2 antiferromagnetic Heisenberg dimerized (alternating) chain. Specifically, the ground state energy and lowest‐lying spectral excitations are examined. The calculation indicates the existence of a gap in the spectrum of the dimerized chain which vanishes only in the limit of a uniform spin chain, in contrast to a recent Green’s function approach. The RG results are in reasonable agreement with numerical extrapolations on the exact eigenvalue spectrum of finite chains of up to 12 spins. Both methods are compared with several other approximate treatments of the Heisenberg system, and tested by comparison with exact results for the spin‐1/2 XY dimerized chain.