Quantum group conjecture and Stripes

Abstract

Keeping in mind our conjecture of modelling cuprates and related systems by quantum groups and our claim that the existence of stripes is intimately related to quantum groups and more strongly is a consequence of the underlying quantum group structure we note that a recent claim that {\em magnetic fluctuations} also displays a one-dimensional character makes our conjecture more viable. The recent strong claim by Mook et al., if true further supports our intuition. For the fluctuations associated with a striped phase are expected to be one-dimensional, whereas the magnetic fluctuations are {\em taken} to display two-dimensional symmetry. It is claimed by Mook et al. that this apparent two-dimensionality results from measurements on twinned crystals, and that similar measurements on substantial detwinned crystals of YBa$_{2}$Cu$_{3}$O$_{6.6}$ reveal the one-dimensional character of the magnetic fluctuations thus making the stripe scenario more stronger, in other words there are also magnetic stripes. As noted before in our conjecture that one of the main reason for quantum groups to model cuprates is that they are directly related to the symmetries of one-dimensional systems. Thus now if the magnetic fluctuations are also shown exhibiting one-dimensional behavior that all the more {\em directly strengthens our conjecture}. However we note that our conjecture is more generic and not tied to the one-dimensional character of the now claimed magnetic fluctuations. Simply the one-dimesional nature of magnetic fluctuations as noted by Mook et al., makes our conjecture more {\em obvious} and clearer.