Collective spin and charge excitations in the $t$-$J$-$U$ model of high-$T_c$ cuprates

Abstract

The $t$-$J$-$U$ model of high-$T_c$ copper-oxide superconductors incorporates both the on-site Coulomb repulsion and kinetic exchange interaction and yields a semi-quantitative description of the static properties of those materials. We extend this analysis to dynamic quantities and address collective spin- and charge excitations in the correlated metallic state of the $t$-$J$-$U$ model. We employ VWF+$1/{\mathcal{N}}_f$ approach that combines the variational wave function (VWF) approach with the expansion in the inverse number of fermionic flavors ($1/{\mathcal{N}}_f$). It is shown that the resonant (paramagnon) contribution to the dynamic magnetic susceptibility remains robust as one interpolates between the Hubbard- and $t$-$J$-model limits, whereas the incoherent continuum undergoes substantial renormalization. Energy of the collective charge mode diminishes as the strong-coupling limit is approached. We also introduce the concept of effective kinetic exchange interaction that allows for a unified interpretation of magnetic dynamics in the Hubbard, $t$-$J$, and $t$-$J$-$U$ models. The results are discussed in the context of recent resonant inelastic $x$-ray scattering experiments for the high-$T_c$ cuprates.

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Cited by in corpus (2)

• Superconductivity in high-$T_c$ and related strongly correlated systems from variational perspective: Beyond mean field theory
• Electron-hole asymmetry of quantum collective excitations in high-$T_c$ copper oxides