Exact many-body wavefunction of the Kondo model with time-dependent interaction strength

We present an exact solution of the nonstationary Schrodinger equation for the Kondo Hamiltonian with a time-dependent spin-exchange coupling $J(t)$ under periodic boundary conditions. Unlike previously studied time-dependent integrable models, which are rooted in the classical Yang-Baxter structure and associated Knizhnik-Zamolodchikov equations, our approach is based on the quantum Knizhnik-Zamolodchikov framework and the quantum Yang-Baxter algebra. We demonstrate that the dynamics is integrable for a class of exchange couplings $J(t)$ of the form $\lambda t + p(t) \pm \sqrt{(\lambda t + p(t))^2 + 4/3}$, where $p(t)$ is an arbitrary periodic function, and construct the corresponding many-body wavefunction. We also discuss extensions to other one-dimensional integrable models with linear dispersion, such as Gross-Neveu and Thirring. Our results broaden the domain of time-dependent integrability to a genuinely quantum class of models and provide a new platform for exploring coherent nonequilibrium dynamics in strongly correlated systems.