Density matrix formulation for quantum renormalization groups

A generalization of the numerical renormalization-group procedure used first by Wilson for the Kondo problem is presented. It is shown that the most important requirement in implementing the renormalization group is that the Hamiltonian of the block is not the object to be diagonalized; instead the density matrix of the block, obtained from the ground state of a superblock containing the block and an environment, should be diagonalized to find the most important states of the block.