Density matrix renormalization group approach to an asymptotically free model with bound states

We apply the density matrix renormalization group (DMRG) method to the two- dimensional delta function potential which is a simple quantum mechanical m odel with asymptotic freedom and formation of bound states. The system bloc k and the environment block of the DMRG contain the low energy and high ene rgy degrees of freedom, respectively. The ground state energy and the lowes t excited states are obtained with very high accuracy. We compare the DMRG method with the similarity renormalization group method and propose its gen eralization to field theoretical models in high energy physics.