Stability of the bulk gap for frustration-free topologically ordered quantum lattice systems
Mathematical Physics
2023-03-10 v3 Strongly Correlated Electrons
math.MP
Quantum Physics
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 Hamiltonians uniform in the system size. To obtain this result, we adapt the Bravyi-Hastings-Michalakis strategy to the GNS representation of the infinite-system ground state.
Keywords
Cite
@article{arxiv.2102.07209,
title = {Stability of the bulk gap for frustration-free topologically ordered quantum lattice systems},
author = {Bruno Nachtergaele and Robert Sims and Amanda Young},
journal= {arXiv preprint arXiv:2102.07209},
year = {2023}
}
Comments
Added Section 3.4 with an additional result; streamlined the exposition; updated references