Hole and spin dynamics in an anti-ferromagnet close to half filling

TL;DR

This paper develops a conserving diagrammatic method to analyze charge and spin dynamics in the doped Fermi-Hubbard model, revealing how doping affects magnetic polarons, magnon spectra, and pseudogap phenomena.

Contribution

It introduces a new systematic diagrammatic approach to study the interplay of charge and spin in strongly correlated materials near half filling.

Findings

Doping creates four magnetic polaron hole pockets in the Brillouin zone.

Magnon spectra soften and dampen with increased hole doping.

The response to lattice modulation explains experimental differences linked to pseudogap physics.

Abstract

The interplay between charge and spin dynamics is at the heart of strongly correlated materials. Inspired by recent quantum simulation experiments, we develop a conserving diagrammatic method to describe the Fermi-Hubbard model for strong repulsion and small hole doping away from the half-filled anti-ferromagnetic ground state. We show that doping leads to four hole pockets in the Brillouin zone formed by magnetic polarons, which become increasingly damped with hole concentration. Likewise, the magnon spectrum of the anti-ferromagnet softens and dampens with doping due to hole-induced magnetic frustration. This gives rise to a suppression of the anti-ferromagnetic correlations in agreement with recent experiments. We then calculate the response of the system to a lattice modulation and recover the qualitative difference between in-phase and out-of-phase modulations seen in experiments, which was interpreted as signs of pseudogap physics. Our results indicate that the complex competition between spin and charge degrees of freedom and the emergence of the pseudogap phase may be usefully analyzed for small dopings, where systematic theories can be developed.