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Condensed Matter > Strongly Correlated Electrons
Title: On tensor network representations of the (3+1)d toric code
(Submitted on 31 Dec 2020 (v1), last revised 7 Dec 2021 (this version, v2))
Abstract: We define two dual tensor network representations of the (3+1)d toric code ground state subspace. These two representations, which are obtained by initially imposing either family of stabilizer constraints, are characterized by different virtual symmetries generated by string-like and membrane-like operators, respectively. We discuss the topological properties of the model from the point of view of these virtual symmetries, emphasizing the differences between both representations. In particular, we argue that, depending on the representation, the phase diagram of boundary entanglement degrees of freedom is naturally associated with that of a (2+1)d Hamiltonian displaying either a global or a gauge $\mathbb Z_2$-symmetry.
Submission history
From: Clement Delcamp [view email][v1] Thu, 31 Dec 2020 14:44:38 GMT (1035kb,D)
[v2] Tue, 7 Dec 2021 09:35:10 GMT (1246kb,D)
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