Exact diagonalization RIXS studies of the doped 1d t₁-t₂-J model at the O K-edge

Resonant inelastic x-ray scattering (RIXS) is a novel spectroscopic method for probing charge and spin excitations in quantum magnets. In one dimension, where quantum fluctuations are most prominent, a system of interacting electrons can support fractionalized spinless charge excitations (holons) and chargeless spin excitation (spinons). Currently, X-ray spectroscopic techniques such as RIXS can excite the O K-edge core electrons of correlated quantum magnets to probe the physical nature of the above mentioned spin-charge separated state. Using exact diagonalization we investigate the O K-edge RIXS response of the one dimensional antiferromagnetic spin chain compound with nearest and next-nearest neighbor hoppings. We also study the spin-anisotropic version of the same model. Interaction of the core electrons with the X-rays generate multi-spinon excitations in the RIXS spectrum, for example in strontium copper oxide. We find that the RIXS spectrum of the t₁-t₂-J model with spin anisotropy presents a rich source of physical information, including allowing us to identify microscopic pathways for how the quantum spin fluctuations control the appearance of the four spinon excitations observed in the isotropic O K-edge spectrum.