The Density Matrix Renormalization Group for Fermion Systems

We discuss techniques of the density matrix renormalization group and their application to interacting fermion systems in more than one dimension. We show numerical results for equal--time spin--spin and singlet pair field correlation functions, as well as the spin gap for the Hubbard model on two chains. The system is a gapped spin liquid at half--filling and shows weak algebraic $d$-wave--like pair field correlations away from half--filling.