Exotic topological order in fractal spin liquids
By B. Yoshida. 2013
213 citations recorded by the source corpus.
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 stringlike 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.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/e0740b740fee2c3a6834f5192b4b76f1224f11d4
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In Atomic and Molecular Physics, and Optics
In Condensed Matter Physics
Citations in the corpus
- Fractons (2018, background): “[10] Beni Yoshida, “Exotic topological order in fractal spin liquids,” Phys.”
- Generalized Symmetries in Condensed Matter (2022, unknown): “For example, it can be a fractal (90, 91).”
- Subdimensional Particle Structure of Higher Rank U(1) Spin Liquids (2016, methodology): “0. Writing down the gauge invariant quantity with the fewest number of derivatives, the magnetic eld in this case was shown10 to also be given by a rank 2 symmetric tensor: B ij = iab jcd @ a cA bd (14) which appears to obey @ iBij = 0. However, once again, due to the compactness of A, we can have ”
- Quantum memories at finite temperature (2014, background): “Topological quantum field theories, and extensions thereupon (Haah, 2011; Hamma et al., 2005c; Walker and Wang, 2012; Yoshida, 2013) give rise to classes of models that are of interest in the field of quantum memories.”
- Towards Classification of Fracton Phases: The Multipole Algebra (2018, background): “Some of the original works on fractal phases [3,5,80] use the language of polynomials over the finite fields.”
- Fracton phases of matter (2020, background): “These unusual new particles were first encountered in certain exactly-solvable three-dimensional spin and Majorana models [1–4, 6– 8], but have since been shown to arise in contexts ranging from topological crystalline defects [9] to plaquette-ordered paramagnets [10] (see also precursor work in Ref”
- Fracton Topological Order, Generalized Lattice Gauge Theory and Duality (2016, background): “Type II fracton phases, such as Haah’s code [16] and related models [17], have fracton excitations that appear at the corners of fractal operators [19].”