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

Abstract

Self-energy corrections due to fermion-magnon interaction are studied in the antiferromagnetic state of the $t-t^{\prime }-t^{\prime \prime }$ 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 $U,t^{\prime },t^{\prime \prime }$, 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 $\mathbf{k}=(0,0)$, as seen in cuprates. For intermediate $U$, 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 $t^{\prime }$, 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 $\mathrm{S}{\mathrm{r}}_2\mathrm{Cu}{\mathrm{O}}_2\mathrm{C}{\mathrm{l}}_2$.

arXiv comment11 pages, 17 figures

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• High energy kink in the dispersion of a hole in an antiferromagnet -- double-occupancy effects on electronic excitations
• Spin waves in the AF state of the $t$-$t^{\prime }$ Hubbard model on the fcc lattice: competing interactions, frustration, and instabilities
• Hole and electron dynamics in the triangular-lattice antiferromagnet -- interplay of frustration and spin fluctuations
• Spin-charge and spin-orbital coupling effects on spin dynamics in ferromagnetic manganites
• Coupled spin-orbital fluctuations in a three orbital model for $4d$ and $5d$ oxides with electron fillings $n=3,4,5$ -- Application to $\mathrm{NaOs}{\mathrm{O}}_3$, $\mathrm{C}{\mathrm{a}}_2\mathrm{Ru}{\mathrm{O}}_4$, and $\mathrm{S}{\mathrm{r}}_2\mathrm{Ir}{\mathrm{O}}_4$