Stability of the bulk gap for frustration-free topologically ordered quantum lattice systems
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Department of Mathematics, University of ArizonaIssue Date
2024-02-03Keywords
46L6081Q15
82B10
82B20
Bulk gap
Gapped ground state
GNS representation
Spectral gap stability
Topological insulator
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Springer Science and Business Media B.V.Citation
Nachtergaele, B., Sims, R., & Young, A. (2024). Stability of the bulk gap for frustration-free topologically ordered quantum lattice systems. Letters in Mathematical Physics, 114(1), 24.Journal
Letters in Mathematical PhysicsRights
© The Author(s) 2024. This article is licensed under a Creative Commons Attribution 4.0 International License.Collection Information
This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.Abstract
We prove that uniformly small short-range perturbations do not close the bulk gap above the ground state of frustration-free quantum spin systems that satisfy a standard local topological quantum order condition. In contrast with earlier results, we do not require a positive lower bound for finite-system spectral gaps uniform in the system size. To obtain this result, we extend the Bravyi–Hastings–Michalakis strategy so it can be applied to perturbations of the GNS Hamiltonian of the infinite-system ground state. © The Author(s) 2024.Note
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Except where otherwise noted, this item's license is described as © The Author(s) 2024. This article is licensed under a Creative Commons Attribution 4.0 International License.