Spinon excitation spectra of the $J_1$-$J_2$ 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 $J_{2} = 0.25 J_{1}$ and an onset of incommensurability in the dispersion relation at $J_{2} = 9 / 17 J_{1}$ [as in S. Brehmer \emph{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.

Spinon excitation spectra of the $J_{1}$ - $J_{2}$ chain from analytical calculations in the dimer basis and exact diagonalization

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Spinon excitation spectra of the $J_{1}$ - $J_{2}$ chain from analytical calculations in the dimer basis and exact diagonalization

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Spinon excitation spectra of the J1J1​-J2J2​ chain from analytical calculations in the dimer basis and exact diagonalization

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Spinon excitation spectra of the J1J1​-J2J2​ chain from analytical calculations in the dimer basis and exact diagonalization

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Spinon excitation spectra of the $J_{1}$ - $J_{2}$ chain from analytical calculations in the dimer basis and exact diagonalization

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Spinon excitation spectra of the $J_{1}$ - $J_{2}$ chain from analytical calculations in the dimer basis and exact diagonalization

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