Entanglement entropy of higher rank topological phases

Abstract

We study entanglement entropy of unusual ${\mathbb{Z}}_N$ topological stabilizer codes which admit fractional excitations with restricted mobility constraint in a manner akin to fracton topological phases. It is widely known that the sub-leading term of the entanglement entropy of a disk geometry in conventional topologically ordered phases is related to the total number of the quantum dimension of the fractional excitations. We show that, in our model, such a relation does not hold, i.e, the total number of the quantum dimension varies depending on the system size, whereas the sub-leading term of the entanglement entropy takes a constant number irrespective to the system size. We give a physical interpretation of this result in the simplest case of the model. More thorough analysis on the entanglement entropy of the model on generic lattices is also presented.

arXiv comment35 pages, 11 figures

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