Magnon Excitations of Cuprate Materials beyond Spin Wave Theory

Spin wave theory, in particular at lowest order, is often used to explain the results of scattering experiments such as inelastic neutron scattering and resonant inelastic X-ray scattering. However, this approach has limitations in accounting for large quantum fluctuations and possible fractional excitations beyond magnon interactions. To address this, we employ a large-scale matrix product state method to compute excitation spectra for an effective spin model on the square lattice relevant to various cuprate materials. When comparing our results with experimental data and spin wave theory for cuprates, such as La$_2$CuO$_4$, we observe a significant disparity in the strength of Hubbard-parameterized interactions. An empirical relation is derived in terms of the interaction strength and data from experimental measurements to obtain a better estimate of the Hubbard parameter. Our simulations are in good agreement with ab initio studies of La$_2$CuO$_4$ and a modified spin wave theory analysis. Furthermore, we will discuss potential application of our approach to a broader range of cuprate materials governed by the Hubbard model.