Eur. Phys. J. B (2014) 87: 229
https://doi.org/10.1140/epjb/e2014-50472-x

Regular Article

Spinon excitation spectra of the J₁-J₂ chain from analytical calculations in the dimer basis and exact diagonalization

LPTMS, Univ. Paris-Sud and CNRS, UMR 8626, 91405 Orsay, France

^a e-mail: guillaume.roux@u-psud.fr

Received: 11 July 2014
Published online: 7 October 2014

Abstract

The excitation spectrum of the frustrated spin-1/2 Heisenberg chain is reexamined using variational and exact diagonalization calculations. We show that the overlap matrix of the short-range resonating valence bond states basis can be inverted which yields tractable equations for single and two spinons excitations. Older results are recovered and new ones, such as the bond-state dispersion relation and its size with momentum at the Majumdar-Ghosh point are found. In particular, this approach yields a gap opening at J₂ = 0.25J₁ and an onset of incommensurability in the dispersion relation at J₂ = 9/17J₁ as in [S. Brehmer et al., J. Phys.: Condens. Matter 10, 1103 (1998)]. These analytical results provide a good support for the understanding of exact diagonalization spectra, assuming an independent spinons picture.