  We propose an analytic response theory for the density matrix renormalization
group whereby response properties correspond to analytic derivatives of density
matrix renormalization group observables with respect to the applied
perturbations. Both static and frequency-dependent response theories are
formulated and implemented. We evaluate our pilot implementation by calculating
static and frequency dependent polarizabilities of short oligo-di-acetylenes.
The analytic response theory is competitive with dynamical density matrix
renormalization group methods and yields significantly improved accuracies when
using a small number of density matrix renormalization group states. Strengths
and weaknesses of the analytic approach are discussed.
