Exotic topological order in fractal spin liquids

TL;DR

This paper introduces a new class of three-dimensional fractal spin liquids with topological order, characterized by fractal objects and algebraic symmetries, which could enhance quantum information storage.

Contribution

It presents a novel class of fractal spin liquids with unique topological properties beyond traditional topological quantum field theory descriptions.

Findings

Ground states involve condensation of fractal objects with algebraic symmetries

Models exhibit stability against local perturbations

Potential for maximal quantum information storage in local spin systems

Abstract

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 particular class of three-dimensional models proposed in this paper may potentially saturate quantum information storage capacity for local spin systems.