Disentangling multi-spin dynamic correlations in the Heisenberg spin-$\frac{1}{2}$ chain

Abstract

Higher-order correlations are essential for understanding exotic phases and uncovering universal aspects of quantum dynamics. While inelastic neutron scattering provides well-established access to two-particle correlations, measuring correlations in solids involving more than two particles remains a major challenge. Focusing on magnetic excitations in the Heisenberg spin-$\frac{1}{2}$ chain, we demonstrate that resonant inelastic X-ray scattering (RIXS) can selectively probe multi-spin dynamical correlations by exciting distinct intermediate states through energy detuning. Through theoretical modeling, we isolate the two- and multi- spin responses, and establish that: (i) The resonant energies of the two- and multi- spin dynamical correlations are separated by $\approx \frac{3}{4}J$; implying that the multi-spin part of the cross-section comes from intermediate states that contain spin flips; (ii) The spectral weight of the two-spin channel exhibits a Lorentzian resonant energy profile consistent with a single dominant electronic configuration, whereas the multi-spin channel response shows a Gaussian-like profile, implying contributions from multiple intermediate spin configurations. These characteristics are reproduced by exact diagonalization of the $t-J$ Hamiltonian, which further reveals that the widths of Lorentzian and Gaussian resonant energy profiles depend primarily on core-hole lifetime ($Γ/2$) and $\frac{2J}Γ$, respectively. Controlled access to multi-spin dynamics, using RIXS energy detuning as a knob, can open new pathways to explore many-body dynamics in quantum materials.