# Stability of ground state degeneracy to long-range interactions

@inproceedings{Lapa2021StabilityOG, title={Stability of ground state degeneracy to long-range interactions}, author={Matthew F. Lapa and Michael A. Levin}, year={2021} }

We show that some gapped quantum many-body systems have a ground state degeneracy that is stable to long-range (e.g., power-law) perturbations, in the sense that any ground state energy splitting induced by such perturbations is exponentially small in the system size. More specifically, we consider an Ising symmetrybreaking Hamiltonian with several exactly degenerate ground states and an energy gap, and we then perturb the system with Ising symmetric long-range interactions. For these models we… Expand

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