  Quantum string, which was brought into discussion recently as a model for the
stripe phase in doped cuprates, is simulated by means of the
density-matrix-renormalization-group method. String collides with adjacent
neighbors, as it wonders, owing to quantum zero-point fluctuations. The energy
cost due to the collisions is our main concern. Embedding a quantum string
between rigid walls with separation d, we found that for sufficiently large d,
collision-induced energy cost obeys the formula \sim exp (- A d^alpha) with
alpha=0.808(1), and string's mean fluctuation width grows logarithmically \sim
log d. Those results are not understood in terms of conventional picture that
the string is `disordered,' and only the short-wave-length fluctuations
contribute to collisions. Rather, our results support a recent proposal that
owing to collisions, short-wave-length fluctuations are suppressed, but
instead, long-wave-length fluctuations become significant. This mechanism would
be responsible for stabilizing the stripe phase.
