Magnon Spectra of Cuprates beyond Spin Wave Theory

The usual starting point for understanding magnons in cuprate antiferromagnets such as La$_2$CuO$_4$ is a spin model incorporating cyclic exchange, which descends from a one-band Hubbard model, and has parameters taken from fits based on non-interacting spin wave theory. Here we explore whether this provides a reliable description of experiment, using matrix product states (MPS) to calculate magnon spectra beyond spin wave theory. We find that analysis based on low orders of spin wave theory leads to systematic overestimates of exchange parameters, with corresponding errors in estimates of Hubbard $t/U$. Once these are corrected, the ''standard'' model provides a good account of magnon dispersion and lineshape in La$_2$CuO$_4$, but fails to fully capture the continuum observed at high energies. The extension of this analysis to CaCuO$_2$ and Sr$_2$IrO$_4$ is also discussed.