Spin Dynamics from Niu-Kleinman Adiabatic Approach and Slave Boson Mean Field Theory

Abstract: Spin-wave excitations provide a central probe of magnetic order and electronic correlations in strongly correlated materials. In this work, we develop an adiabatic theory of spin dynamics by combining the Niu-Kleinman formalism with Kotliar-Ruckenstein slave-boson theory (NK+KRSB). For each frozen spin configuration, the constrained slave-boson saddle point is solved self-consistently, allowing the Berry-curvature matrix and energy Hessian entering the linearized adiabatic equations of motion to be extracted directly. Applied to the half-filled single-orbital Hubbard model, the resulting spin-wave dispersion shows substantially improved agreement with determinant quantum Monte Carlo benchmarks compared with the random phase approximation and closely approaches results from the time-dependent Gutzwiller approximation. We further extend the method to a two-orbital model of $\mathrm{La}_2\mathrm{NiO}_4$, demonstrating its applicability to realistic multi-orbital correlated systems. Because the approach only requires saddle-point solutions near the magnetic ground state, it remains computationally efficient while incorporating strong-correlation effects beyond conventional weak-coupling descriptions, providing a practical framework for studying low-energy spin excitations in correlated quantum materials.