The stability of free fermi Hamiltonians

Recent results have shown the stability of frustration-free Hamiltonians to weak local perturbations, assuming several conditions. In this paper, we prove the stability of free fermion Hamiltonians which are gapped and local. These free fermion Hamiltonians are not necessarily frustration-free, but...

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Bibliographic Details
Published in:Journal of mathematical physics 2019-04, Vol.60 (4)
Main Author: Hastings, M. B.
Format: Article
Language:English
Subjects:
Conductance
Fermions
Frustration
Obstructions
Physics
Resistance
Stability
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Summary:Recent results have shown the stability of frustration-free Hamiltonians to weak local perturbations, assuming several conditions. In this paper, we prove the stability of free fermion Hamiltonians which are gapped and local. These free fermion Hamiltonians are not necessarily frustration-free, but we are able to adapt previous work to prove stability. The key idea is to add an additional copy of the system to cancel topological obstructions. We comment on applications to quantization of Hall conductance in such systems.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.5053869