Density Matrix Approach to Local Hilbert Space Reduction

We present a density matrix approach for treating systems with a large or infinite number of degrees of freedom per site with exact diagonalization or the density matrix renormalization group. The method is demonstrated on the 1D Holstein model of electrons coupled to Einstein phonons. In this system, two or three optimized phonon modes per site give results as accurate as with 10-100 bare phonon levels per site.