@article{f81e768c7f5e4cba9f86e19f4cfbe725,
title = "Stability of the bulk gap for frustration-free topologically ordered quantum lattice systems",
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.",
keywords = "46L60, 81Q15, 82B10, 82B20, Bulk gap, GNS representation, Gapped ground state, Spectral gap stability, Topological insulator",
author = "Bruno Nachtergaele and Robert Sims and Amanda Young",
note = "Based upon work supported by the National Science Foundation under grants DMS-1813149 and DMS-21083901 (BN), and the DFG under EXC-2111\u2013390814868 and TRR 352 (Grant: Number: 470903074): Mathematik der Vielteilchen-Quantensysteme und ihrer kollektiven Ph\u00E4nomene (AY). BN and AY acknowledge support of the Erwin Schr\u00F6dinger International Institute for Mathematics and Physics (ESI), where part of this work was carried out during the \u201CTensor Networks: Mathematical Structures and Novel Algorithms\u201D workshop. BN also gratefully acknowledges kind hospitality at the Technical University Munich during the final stages of this work and the Alexander von Humboldt Foundation for support provided through a Carl Friedrich von Siemens Research Award.",
year = "2024",
month = feb,
doi = "10.1007/s11005-023-01767-8",
language = "English (US)",
volume = "114",
journal = "Letters in Mathematical Physics",
issn = "0377-9017",
publisher = "Springer Netherlands",
number = "1",
}