Exotic topological order in fractal spin liquids

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.

18 pages, 10 figures

References in corpus (8)

• Non-Abelian Anyons and Topological Quantum Computation
• Local stabilizer codes in three dimensions without string logical operators
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Topological Quantum Glassiness
• Quantum mechanical and information theoretic view on classical glass transitions
• Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes
• Framework for classifying logical operators in stabilizer codes
• Information storage capacity of discrete spin systems

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