Understanding spin excitations of a doped 1D Mott insulator

The surprising persistence of collective spin excitations upon doping a 2D Mott insulator has
recently been observed in hole- and electron-doped quasi-2D copper oxides. However, the theoretical
understanding of this phenomenon is still lacking. Using exact diagonalization combined with cluster
perturbation theory, we study the evolution of spin excitations with doping, solve both the Hubbard
and t-J models, and analyze the roles of three-site terms and next-nearest-neighbor hopping. Upon
hole doping, we observe broadening of the two-spinon continuum, shift of zero modes, and strong
softening of the one-spinon branch, suggesting that spin excitations in 1D materials such as Sr₂CuO₃
are suppressed upon hole doping in contrast to 2D cuprates. Upon electron doping, we find hardening
similar to that in recent experiments on 2D cuprates. To better understand numerical results, we
adopt strong coupling slave-boson mean-field theory. We show that the mean-field theory is able to
account for the evolution of the spin dynamic structure factor upon doping. This method provides
intuitive insights into spectral features as well as general trends depending on doping levels and
second nearest neighbor hopping, which are valuable to understand future experiments on doped
1D Mott Insulators.