Dispersion of a single hole in the t-J model

The dispersion of a single hole in the t-J model obtained by the exact result of 32 sites and the results obtained by self-consistent Born approximation and the Green function Monte Carlo method can be simply derived by a mean-field theory with d-wave resonating-valence-bond (d-RVB) and antiferromagnetic order parameters. In addition, it offers a simple explanation for the difference observed between those results. The presence of the extended van Hove region at (π,0) is a consequence of the d-RVB pairing instead of the antiferromagnetic order. Results including ${\mathrm{t}}^{|\mathrm{I}\mathrm{H}}$ and ${\mathrm{t}}^{|\mathrm{I}\mathrm{J}}$ are also presented and explained consistently in a similar way.