Electron-hole asymmetry of quantum collective excitations in high-$T_c$ copper oxides

TL;DR

This study systematically compares collective spin and charge excitations in various Hubbard and $t$-$J$ models of high-$T_c$ cuprates, revealing electron-hole asymmetries and model-specific spectral features consistent with experimental data.

Contribution

It introduces a variational wave function approach combined with a fermionic flavor expansion to analyze collective excitations across different models and doping types in high-$T_c$ cuprates.

Findings

Robust paramagnon observed in hole-doped models.

High-energy magnetic peak in $t$-$J$ model not clearly seen in experiments.

Charge excitations show coherent modes with doping-dependent bandwidth.

Abstract

We carry out a systematic study of collective spin- and charge excitations for the canonical single-band Hubbard, $t$-$J$-$U$, and $t$-$J$ models of high-temperature copper-oxide superconductors, both on electron- and hole-doped side of the phase diagram. Recently developed variational wave function approach, combined with the expansion in inverse number of fermionic flavors, is employed. All three models exhibit a substantial electron-hole asymmetry of magnetic excitations, with a robust paramagnon emerging for hole-doping, in agreement with available resonant inelastic $x$-ray scattering data for the cuprates. The $t$-$J$ model yields additional high-energy peak in the magnetic spectrum that is not unambiguously identified in spectroscopy. For all considered Hamiltonians, the dynamical charge susceptibility contains a coherent mode for both hole- and electron doping, with overall bandwidth renormalization controlled by the on-site Coulomb repulsion. Away from the strong-coupling limit, the antiferromagnetic ordering tendency is more pronounced on electron-doped side of the phase diagram.