We compute dynamic spin susceptibilities in the two-dimensional Hubbard model using the method of dual fermions, and we provide a comparison to lattice Monte Carlo and cluster dynamical mean-field theory. We examine the energy dispersion identified by peaks in $\mathrm{Im}\chi (\omega ,q)$, which define spin modes, and we compare the exchange scale and magnon dispersion to neutron experiments on the parent ${\mathrm{La}}_2{\mathrm{CuO}}_4$ cuprate. We present the evolution of the spin excitations as a function of Hubbard interaction strengths and doping, and we explore the particle-hole asymmetry of the spin excitations. We also study the correlation lengths and the spin excitation dispersion peak structure, and we find a Y-shaped dispersion similar to neutron results on doped ${\mathrm{HgBa}}_2{\mathrm{CuO}}_{4+\delta }$.

• Received 24 April 2019
• Revised 24 July 2019

DOI:https://doi.org/10.1103/PhysRevB.100.075123