Quantum-fluctuation-induced collisions and subsequent excitation gap of an elastic string between walls

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.