Henheik Joscha, Teufel Stefan, Wessel Tom
Institute of Science and Technology Austria (IST Austria), Am Campus 1, Klosterneuburg, 3400 Austria.
Mathematisches Institut, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 10, Tübingen, 72076 Germany.
Lett Math Phys. 2022;112(1):9. doi: 10.1007/s11005-021-01494-y. Epub 2022 Jan 18.
Based on a result by Yarotsky (J Stat Phys 118, 2005), we prove that localized but otherwise arbitrary perturbations of weakly interacting quantum spin systems with uniformly gapped on-site terms change the ground state of such a system only locally, even if they close the spectral gap. We call this a of the (LPPL) principle which is known to hold for much more general gapped systems, but only for perturbations that do not close the spectral gap of the Hamiltonian. We also extend this strong LPPL-principle to Hamiltonians that have the appropriate structure of gapped on-site terms and weak interactions only locally in some region of space. While our results are technically corollaries to a theorem of Yarotsky, we expect that the paradigm of systems with a locally gapped ground state that is completely insensitive to the form of the Hamiltonian elsewhere extends to other situations and has important physical consequences.
基于亚罗茨基的一个结果（《统计物理杂志》118卷，2005年），我们证明，对于具有均匀能隙在位项的弱相互作用量子自旋系统，即使局域但任意的微扰会关闭能谱间隙，这种微扰也只会在局部改变该系统的基态。我们将此称为局域化微扰下的基态持久性（LPPL）原理，已知该原理对于更一般的有隙系统成立，但仅适用于不会关闭哈密顿量能谱间隙的微扰。我们还将这个强LPPL原理推广到仅在空间的某些区域局部具有合适的有隙在位项结构和弱相互作用的哈密顿量。虽然我们的结果在技术上是亚罗茨基一个定理的推论，但我们预计具有对其他地方哈密顿量形式完全不敏感的局域有隙基态的系统范式会扩展到其他情况，并具有重要的物理后果。
