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A gapped ground state of a quantum spin system has a natural length scale setby the gap. This length scale governs the decay of correlations. A commonintuition is that this length scale also controls the spatial relaxationtowards the ground state away from impurities or boundaries. The aim of thisarticle is to take a step towards a proof of this intuition. We assume that theground state is frustration-free and invertible, i.e.\ it has no long-rangeentanglement. Moreover, we assume the property that we are aiming to prove forone specific kind of boundary condition; namely open boundary conditions. Thisassumption is also known as the "local topological quantum order" (LTQO)condition. With these assumptions we can prove stretched exponential decay awayfrom boundaries or impurities, for any of the ground states of the perturbedsystem. In contrast to most earlier results, we do not assume that theperturbations at the boundary or the impurity are small. In particular, theperturbed system itself can have long-range entanglement.

Stability of invertible, frustration-free ground states against large perturbations