  We study the application of the density matrix renormalization group (DMRG)
to systems with one-dimensional acoustic phonons. We show how the use of a
local oscillator basis circumvents the difficulties with the long-range
interactions generated in real space using the normal phonon basis. When
applied to a harmonic atomic chain, we find excellent agreement with the exact
solution even when using a modest number of oscillator and block states (a few
times ten). We discuss the use of this algorithm in more complex cases and
point out its value when other techniques are deficient.
