Stability of ground state degeneracy to long-range interactions

Abstract

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 symmetry-breaking 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 prove (1) the stability of the gap, and (2) that the residual splitting of the low-energy states below the gap is exponentially small in the system size. Our proof relies on a convergent polymer expansion that is adapted to handle the long-range interactions in our model. We also discuss applications of our result to several models of physical interest, including the Kitaev p-wave wire model perturbed by power-law density-density interactions with an exponent greater than 1.

33 pages (single column), 2 figures. v2: corrected an error in the previous statement of Theorem 3

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Cited by in corpus (3)

• Bulk-boundary correspondence and singularity-filling in long-range free-fermion chains
• Low-density parity-check codes as stable phases of quantum matter
• Effect of slowly decaying long-range interactions on topological qubits