2025/05/26 by Parameshwar R. Pasnoori, Pasnoori, Parameshwar R. · 2 citations
Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.2505.20125
openalex publication_date 2025/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this letter we consider the time dependent Kondo model where a magnetic impurity interacts with the electrons through a time dependent interaction strength J(t). We develop a new framework based on Bethe ansatz and construct an exact solution to the time-dependent Schrodinger equation. We show that when periodic boundary conditions are applied, the consistency of the solution results in a constraint equation which relates the amplitudes corresponding to a certain ordering of the particles in the configuration space. This constraint equation takes the form of a matrix difference equation, and the associated consistency conditions restrict the interaction strength J(t) for the system to be integrable. For a given J(t) satisfying these constraints, the solution to the matrix difference equations provides the exact many-body wavefunction that satisfies the time-dependent Schrodinger equation. We provide a concrete example of J(t) which satisfies these constraint equations. We show that in this case, the matrix difference equations turn into quantum Knizhnik-Zamolodchikov (qKZ) equations, which are well studied in the literature. The framework developed in this work allows one to probe the non-equilibrium physics of the Kondo model, and being general, it also allows one to solve new class of Hamiltonians with time-dependent interaction strength which are based on quantum Yang-Baxter algebra.