Does frustration describe doping in models for high-temperature superconductors?

Since the discovery of the high-${\mathit{T}}_{\mathit{c}}$ superconductors there has been a revival of interest in frustrated magnetic systems. In this work, we compare predictions of frustrated and doped Hamiltonians by studying the t-J model with one hole and the frustrated Heisenberg J-J’ model. In particular, we compare for both systems the dynamic spin-spin structure factor S(q,ω), and the ${\mathit{B}}_{1\mathit{g}}$ Raman scattering spectrum R(ω) at zero temperature. We observe that, for the t-J model, both quantities are in qualitative agreement with experimental measurements while the corresponding ones for the J-J’ model are not. These results indicate that doped systems cannot be accurately modeled by a purely spin model and that the latter, including the chiral spin states, might not be relevant to describe measurable quantities of the high-${\mathit{T}}_{\mathit{c}}$ materials.