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Entanglement entropy from tensor network states for stabilizer codes

Author(s): He, Huan; Zheng, Yunqin; Bernevig, Bogdan A.; Regnault, Nicolas

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Abstract: In this paper, we present the construction of tensor network states (TNS) for some of the degenerate ground states of three-dimensional (3D) stabilizer codes. We then use the TNS formalism to obtain the entanglement spectrum and entropy of these ground states for some special cuts. In particular, we work out examples of the 3D toric code, the X-cube model, and the Haah code. The latter two models belong to the category of “fracton” models proposed recently, while the first one belongs to the conventional topological phases. We mention the cases for which the entanglement entropy and spectrum can be calculated exactly: For these, the constructed TNS is a singular value decomposition (SVD) of the ground states with respect to particular entanglement cuts. Apart from the area law, the entanglement entropies also have constant and linear corrections for the fracton models, while the entanglement entropies for the toric code models only have constant corrections. For the cuts we consider, the entanglement spectra of these three models are completely flat. We also conjecture that the negative linear correction to the area law is a signature of extensive ground-state degeneracy. Moreover, the transfer matrices of these TNSs can be constructed. We show that the transfer matrices are projectors whose eigenvalues are either 1 or 0. The number of nonzero eigenvalues is tightly related to the ground-state degeneracy.
Publication Date: 15-Mar-2018
Electronic Publication Date: 1-Mar-2018
Citation: He, Huan, Zheng, Yunqin, Bernevig, B Andrei, Regnault, Nicolas. (2018). Entanglement entropy from tensor network states for stabilizer codes. PHYSICAL REVIEW B, 97 (10.1103/PhysRevB.97.125102
DOI: doi:10.1103/PhysRevB.97.125102
ISSN: 2469-9950
EISSN: 2469-9969
Type of Material: Journal Article
Journal/Proceeding Title: PHYSICAL REVIEW B
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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