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

TL;DR

This paper investigates how classical and quantum effects influence quasiparticle dispersion in an antiferromagnetic Hubbard model, revealing key insights into the suppression of quasiparticle weight and phase transitions relevant to cuprate materials.

Contribution

It introduces a comprehensive analysis of self-energy corrections across all interaction strengths, highlighting the role of finite-U induced classical dispersion and the critical U for phase transition, with implications for cuprate superconductors.

Findings

Finite-U classical dispersion suppresses quasiparticle weight near (0,0).

Renormalized AF band gap is about half the classical value at intermediate U.

Critical U_c marks a first-order AF insulator to PM metal transition.

Abstract

Self-energy corrections due to fermion-magnon interaction are studied in the antiferromagnetic state of the $t-t'-t''$ 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 $U,t',t''$, 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 ${\bf k}=(0,0)$, 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 $t'$, 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 $.