Self-energy corrections in an antiferromagnet -- interplay of classical and quantum effects on quasiparticle dispersion

Self-energy corrections due to fermion-magnon interaction are studied in the antiferromagnetic state of the $t-t^{\mathrm{\prime }}-t^{\mathrm{\prime }\mathrm{\prime }}$ Hubbard model within the rainbow (noncrossing) approximation in the full $U$ range from weak to strong coupling. The role of classical (mean-field) features of fermion and magnon dispersion, associated with finite $U,t^{\mathrm{\prime }},t^{\mathrm{\prime }\mathrm{\prime }}$, are examined on quantum corrections to quasiparticle energy, weight, one-particle density of states etc. A finite-$U$ induced classical dispersion term, absent in the $t-J$ model, is found to play an important role in suppressing the quasiparticle weight for states near ${\bf k}=(0,0)$,asseenincuprates\mathrm{.}Forintermediate$U$, the renormalized AF band gap is found to be nearly half of the classical value, and the weak coupling limit is quite non-trivial due to strongly suppressed magnon amplitude. For finite $t^{\mathrm{\prime }}$, the renormalized AF band gap is shown to vanish at a critical interaction strength $U_c$, yielding a spin fluctuation driven first-order AF insulator - PM metal transition. Quasiparticle dispersion evaluated with the same set of Hubbard model cuprate parameters, as obtained from a recent magnon spectrum fit, provides excellent agreement with ARPES data for $\rm Sr_2 Cu O_2 Cl_2 $.