Low-lying excitation spectrum of quantum many-body systems

We present a numerical method for calculating the ground state correlations and low-lying excitations in a discrete and finite many-body system. The method combines the advantages of real space and momentum space renormalization group ideas and is similar in many respects to the correlated basis functions perturbation theory, but is nonperturbative in nature. To illustrate the method, we apply it to the one-dimensional Heisenberg antiferromagnetic spin-½ chain.