  An elastic string embedded between rigid walls is simulated by means of the
density-matrix renormalization group. The string collides against the walls
owing to the quantum-mechanical zero-point fluctuations. Such ``quantum
entropic'' interaction has come under thorough theoretical investigation in the
context of the stripe phase observed experimentally in doped cuprates. We found
that the excitation gap opens in the form of exponential singularity DeltaE ~
exp(-Ad^sigma) (d: wall spacing) with the exponent sigma =0.6(3), which is
substantially smaller than the meanfield value sigma=2. That is, the excitation
gap is much larger than that anticipated from meanfield, suggesting that the
string is subjected to robust pinning potential due to the quantum collisions.
This feature supports Zaanen's ``order out of disorder'' mechanism which would
be responsible to the stabilization of the stripe phase.
