The Rubinstein-Duke model for polymer reptation is analyzed by means of den
sity matrix renormalization techniques. It is found that the crossover in t
he scaling behavior of polymer renewal time (or viscosity) arises from the
competing effect of the contribution due to tube length fluctuations and hi
gher-order corrections, which are of opposite sign. Experiments which ought
to emphasize both contributions are suggested. The exponent describing the
subleading scaling behavior of the diffusion coefficient is also investiga
ted.