1302.6248 (Beni Yoshida)

Exotic topological order in fractal spin liquids    [PDF]

Beni Yoshida

We present a large class of three-dimensional spin models that possess topological order with stability against local perturbations, but are beyond description of topological quantum field theory. Conventional topological spin liquids, on a formal level, may be viewed as condensation of string-like extended objects with discrete gauge symmetries, being at fixed points with continuous scale symmetries. In contrast, ground states of fractal spin liquids are condensation of highly-fluctuating fractal objects with certain algebraic symmetries, corresponding to limit cycles under real-space renormalization group transformations which naturally arise from discrete scale symmetries of underlying fractal geometries. A theoretical framework for unified analysis on physical properties of fractal spin liquids is presented, which is applicable to all the previously known examples.

View original: http://arxiv.org/abs/1302.6248