Quantum-fluctuation-induced repulsive interaction of a quantum string between walls

Abstract

A 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 wanders, 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 $\ensuremath{\sim}\mathrm{exp}(\ensuremath{-}{\mathrm{Ad}}^{\ensuremath{\alpha}})$ with $\ensuremath{\alpha}=0.808(1),$ and the string's mean fluctuation width grows logarithmically $\ensuremath{\sim}\mathrm{log}d.$ Those results are not understood in terms of a conventional picture that the string is ``disordered,'' and only short-wavelength fluctuations contribute to collisions. Rather, our results support a recent proposal that owing to collisions, short-wavelength fluctuations are suppressed, but instead, long-wavelength fluctuations become significant. This mechanism would be responsible for stabilizing the stripe phase.