Fluctuating the magnetic slave-boson mean-field: analysis of charge modulations in an antiferromagnetic background

The richness of the cuprate phase diagram and the intricate relations between the different types of order call for computationally cheap and stable methods that also allow for the inspection of symmetry-broken ground states. Aiming at the single-orbital Hubbard Hamiltonian as a minimal cuprate model, we present a fluctuation analysis around magnetic saddle points in the spin-rotation invariant Kotliar-Ruckenstein slave-boson approach. We derive the effective second-order field theory on top of an antiferromagnetic parent state. Spin and charge correlation functions are analyzed for the stability of the phase diagram and the magnon spectra are discussed. Further, we find different signatures of charge order at intermediate to high interaction strengths.