  The density matrix renormalization group is applied to a relativistic complex
scalar field at finite chemical potential. The two-point function and various
bulk quantities are studied. It is seen that bulk quantities do not change with
the chemical potential until it is larger than the minimum excitation energy.
The technical limitations of the density matrix renormalization group for
treating bosons in relativistic field theories are discussed. Applications to
other relativistic models and to nontopological solitons are also suggested.
