%0 Generic %1 bachmann2021stability %A Bachmann, Sven %A De Roeck, Wojciech %A Donvil, Brecht %A Fraas, Martin %D 2021 %K information quantum %T Stability against large perturbations of invertible, frustration-free ground states %U http://arxiv.org/abs/2110.11194 %X A gapped ground state of a quantum spin system has a natural length scale set by the gap. This length scale governs the decay of correlations. A common intuition is that this length scale also controls the spatial relaxation towards the ground state away from impurities or boundaries. The aim of this article is to take a step towards a proof of this intuition. To make the problem more tractable, we assume that there is a unique ground state that is frustration-free and invertible (i.e. no long-range entanglement). Moreover, we assume the property that we are aiming to prove for one specific kind of boundary condition; namely open boundary conditions. With these assumptions we can prove stretched exponential decay away from boundaries for any boundary conditions or (large) perturbations and for all ground states of the perturbed system. In particular, the perturbed system itself can certainly have long-range entanglement.

@misc{bachmann2021stability, abstract = {A gapped ground state of a quantum spin system has a natural length scale set by the gap. This length scale governs the decay of correlations. A common intuition is that this length scale also controls the spatial relaxation towards the ground state away from impurities or boundaries. The aim of this article is to take a step towards a proof of this intuition. To make the problem more tractable, we assume that there is a unique ground state that is frustration-free and invertible (i.e. no long-range entanglement). Moreover, we assume the property that we are aiming to prove for one specific kind of boundary condition; namely open boundary conditions. With these assumptions we can prove stretched exponential decay away from boundaries for any boundary conditions or (large) perturbations and for all ground states of the perturbed system. In particular, the perturbed system itself can certainly have long-range entanglement.}, added-at = {2021-10-22T16:56:46.000+0200}, author = {Bachmann, Sven and De Roeck, Wojciech and Donvil, Brecht and Fraas, Martin}, biburl = {https://www.bibsonomy.org/bibtex/29cada17b44d35d539c3b51fdb9f34803/gzhou}, description = {Stability against large perturbations of invertible, frustration-free ground states}, interhash = {bf1057b8821ecae8a133daaa9fcbdf68}, intrahash = {9cada17b44d35d539c3b51fdb9f34803}, keywords = {information quantum}, note = {cite arxiv:2110.11194Comment: 21 pages}, timestamp = {2021-10-22T16:56:46.000+0200}, title = {Stability against large perturbations of invertible, frustration-free ground states}, url = {http://arxiv.org/abs/2110.11194}, year = 2021 }