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Fracton topological order via coupled layers · Around

2017

Fracton topological order via coupled layers

Ma, Han, Lake, Ethan, Chen, Xie et al.

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In this work, we develop a coupled layer construction of fracton topological orders in $d=3$ spatial dimensions.

These topological phases have sub-extensive topological ground-state degeneracy and possess excitations whose movement is restricted in interesting ways.
Our coupled layer approach is used to construct several different fracton topological phases, both from stacked layers of simple $d=2$ topological phases and from stacks of $d=3$ fracton topological phases.
This perspective allows us to shed light on the physics of the X-cube model recently introduced by Vijay, Haah, and Fu, which we demonstrate can be obtained as the strong-coupling limit of a coupled three-dimensional stack of toric codes.

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More precisely, we are describing non-invertible topological orders, a class that excludes symmetry-protected topological phases such as the S = 1 S=1 Haldane chain and topological band insulators, as well as integer topological phases such as the integer quantum Hall liquids. We note that in some cases the topological excitations are not point objects, but can be localized to a c c -dimensional subspace where c < d c<d

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M. Pretko, (2016a) , arXiv:1604.05329

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J. Haah, Phys. Rev. B 89

2014

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S. Vijay, J. Haah, and L. Fu, Phys. Rev. B 92

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S. Vijay, J. Haah, and L. Fu, (2016) , arXiv:1603.04442

2016

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