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

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 J(2) = 0.25J(1) and an onset of incommensurability in the dispersion relation at J(2) = 9/17J(1) 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.