Dynamics of a Moving Kondo Impurity in the Spin Chain

The problem of a single impurity interacting with a bath has been considered in various systems. Here we consider the single hole limit of a one-dimensional two-band model, which is relevant to the physics of cuprates. Combining Galilean transformation and density matrix renormalization group (DMRG) method, we obtain not only the ground state properties but also the low-energy dispersion. It is shown that, with an increasing Kondo coupling JK, the total momentum of the ground state has a crossover from 0 to π/2, which corresponds to the t-J physics in the large JK limit. Simultaneously, the spin of the hole will be screened with antiferromagnetic coupling JK. This method can be easily applied to other single-impurity problems in one dimension and ladder systems, which opens the door to study the dynamics of a single particle coupled to a bath.