Impurities and boundaries for a class of gapped ground states

Abstract: In the last two decades, a lot of rigorous results have been proven for quantum ground states protected by a spectral gap in their Hamiltonian. Think for example of decay of correlations, the topological classification of states, and area laws of entanglement. For all of those results, the spectral gap is a necessary input, both on the conceptual and on the technical level. Imagine now that we consider such a gapped Hamiltonian that is perturbed locally by a term that is not small, such that we certainly cannot hope to preserve the global gap. Common sense dictates that, far away from the perturbation, the ground state should not be seriously affected by this perturbation. While we cannot prove this in the generality in which it should be true, I will describe some results that go in this direction.

mathematical physics

Audience: researchers in the discipline

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