Spectroscopic signatures of next-nearest-neighbor hopping in the charge and spin dynamics of doped one-dimensional antiferromagnets

We study the impact of next-nearest-neighbor (NNN) hopping on the low-energy collective excitations of strongly correlated doped antiferromagnetic cuprate spin chains. Specifically, we use exact diagonalization and the density matrix renormalization group method to study the single-particle spectral function, the dynamical spin and charge structure factors, and the Cu L-edge resonant inelastic X-ray scattering (RIXS) intensity of the doped t-t′-J model for a set of t′ values. We find evidence that the spin and charge degrees of freedom of the doped holes are not strictly separated anymore as |t′| increases and identify the consequences of this in the dynamical response functions. The inclusion of NNN hopping couples the spinon and holon excitations, resulting in the formation of a spin polaron, where a ferromagnetic spin-polarization cloud dresses the doped carrier. The spin polaron manifests itself as additional spectral weight in the dynamical correlation functions, which appear simultaneously in the spin-and charge-sensitive channels. We also demonstrate that RIXS can provide a unique view of the spin polaron, due to its sensitivity to both the spin and charge degrees of freedom.