Dispersion of a single hole in an antiferromagnet

We revisit the problem of the dispersion of a single hole injected into a quantum antiferromagnet. We applied a spin-density-wave formalism extended to a large number of orbitals and obtained an integral equation for the full quasiparticle Green’s function in the self-consistent “noncrossing” Born approximation. We found that for (Formula presented), the bare fermionic dispersion is completely overshadowed by the self-energy corrections. In this case, the quasiparticle Green’s function contains a broad incoherent continuum which extends over a frequency range of (Formula presented). In addition, there exists a narrow region of width (Formula presented) below the top of the valence band, where the excitations are mostly coherent, though with a small quasiparticle residue (Formula presented). The top of the valence band is located at (Formula presented). We found that the form of the fermionic dispersion, and, in particular, the ratio of the effective masses near (Formula presented) strongly depend on the assumptions one makes for the form of the magnon propagator. We argue in this paper that two-magnon Raman scattering as well as neutron-scattering experiments strongly suggest that the zone-boundary magnons are not free particles since a substantial portion of their spectral weight is transferred into an incoherent background. We modeled this effect by introducing a cutoff (Formula presented) in the integration over magnon momenta. We found analytically that for small (Formula presented) the strong-coupling solution for the Green’s function is universal, and both effective masses are equal to (Formula presented). We further computed the full fermionic dispersion for (Formula presented) relevant for (Formula presented), and (Formula presented) and found not only that the masses are both equal to (Formula presented), but also that the energies at (Formula presented) and (Formula presented) are equal, the energy at (Formula presented) is about half of that at (Formula presented), and the bandwidth for the coherent excitations is around (Formula presented). All of these results are in full agreement with the experimental data. Finally, we found that weakly damped excitations only exist in a narrow range around (Formula presented). Away from the vicinity of (Formula presented), the excitations are overdamped, and the spectral function possesses a broad maximum rather than a sharp quasiparticle peak. This last feature was also reported in photoemission experiments.