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arXiv · 2302.11468

Entanglement entropy of higher rank topological phases

Hiromi Ebisu
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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.

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Hiromi Ebisu. 2023-02-22. Entanglement entropy of higher rank topological phases. https://doi.org/10.1103/physrevb.110.045146

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