Wilbur Shirley, Kevin Slagle, Xie Chen
SciPost Phys. 6, 015 (2019) ·
published 31 January 2019

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Fracton models exhibit a variety of exotic properties and lie beyond the
conventional framework of gapped topological order. In a previous work, we
generalized the notion of gapped phase to one of foliated fracton phase by
allowing the addition of layers of gapped twodimensional resources in the
adiabatic evolution between gapped threedimensional models. Moreover, we
showed that the Xcube model is a fixed point of one such phase. In this paper,
according to this definition, we look for universal properties of such phases
which remain invariant throughout the entire phase. We propose multipartite
entanglement quantities, generalizing the proposal of topological entanglement
entropy designed for conventional topological phases. We present arguments for
the universality of these quantities and show that they attain nonzero
constant value in nontrivial foliated fracton phases.