Stability of the bulk gap for frustration-free topologically ordered quantum lattice systems

• URL: http://arxiv.org/abs/2102.07209v3
• Date: Thu, 9 Mar 2023 10:15:09 GMT
• Title: Stability of the bulk gap for frustration-free topologically ordered quantum lattice systems
• Authors: Bruno Nachtergaele, Robert Sims, Amanda Young
• Abstract summary: We prove that uniformly small short-range perturbations do not close the bulk gap above the ground state of frustration-free quantum spin systems. We do not require a positive lower bound for finite-system Hamiltonians uniform in the system size.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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