Spin and bond-charge excitation spectra in correlated electron systems near an antiferromagnetic phase

Magnetic and bond-charge interactions can arise from the same microscopic interaction. Motivated by this observation, we compute magnetic and bond-charge excitation spectra on an equal footing by introducing a simple effective model on a square lattice, which describes antiferromagnetic and $d$-wave superconducting phases around half-filling on the electron-doped side. The magnetic excitation spectrum $\mathrm{Im}\chi (q,\omega )$ has strong weight around $q=(\pi ,\pi )$ in low energy, and its intensity map exhibits a pencil-tip-like shape in $q\text{−}\omega$ space. Around $q=(0,0)$ magnetic excitations show a steep dispersion toward the $(\pi ,\pi )$ and $(\pi ,0)$ directions, which is very similar to a spin-wave dispersion although the system is nonmagnetic. Bond-charge excitations are characterized by four different symmetries and studied for all possible couplings. Bond-charge fluctuations with three different symmetries have large spectral weight around $q=(\pi ,\pi )$ in a relatively low-energy region and extend widely more than the magnetic excitation spectrum. The $d$-wave symmetry of bond-charge excitations also has sizable spectral weight along the direction $(\pi /2,\pi /2)\text{−}(0,0)\text{−}(\pi /2,0)$ in a low-energy region and exhibits softening around $q\approx (0.5\pi ,0)$, whereas no such softening is present in the other symmetries. These results capture the essential features observed in electron-doped cuprates and may motivate an experimental test of bond-charge excitations around $q=(\pi ,\pi )$ on top of the strong magnetic excitations there as well as additional softening in the $d$-wave channel in the $(\pi ,\pi )\text{−}(\pi /2,\pi /2)$ region at low temperatures near the magnetic phase. We extend the present analysis to the hole-doped side and highlight a contrast to the electron-doped side, which includes incommensurate correlations, electronic nematic correlations, and spin and bond-charge resonance modes in the superconducting state.