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Condensed Matter > Strongly Correlated Electrons
Title: On the stability of topological order in tensor network states
(Submitted on 30 Dec 2020 (v1), last revised 29 Dec 2021 (this version, v2))
Abstract: We construct a tensor network representation of the 3d toric code ground state that is stable to a generating set of uniform local tensor perturbations, including those that do not map to local operators on the physical Hilbert space. The stability is established by mapping the phase diagram of the perturbed tensor network to that of the 3d Ising gauge theory, which has a non-zero finite temperature transition. More generally, we find that the stability of a topological tensor network state is determined by the form of its virtual symmetries and the topological excitations created by virtual operators that break those symmetries. In particular, a dual representation of the 3d toric code ground state, as well as representations of the X-cube and cubic code ground states, for which point-like excitations are created by such operators, are found to be unstable.
Submission history
From: Dominic Williamson [view email][v1] Wed, 30 Dec 2020 22:28:43 GMT (119kb,D)
[v2] Wed, 29 Dec 2021 13:37:23 GMT (260kb,D)
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