article published yes Sven Joscha Henheik author 31d731d7-d235-11ea-ad11-b50331c8d7fb0000-0003-1106-327X Stefan Teufel author Tom Wessel author GradSch department LaEr department Random matrices beyond Wigner-Dyson-Mehta project 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 strong version of the local perturbations perturb locally (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. https://research-explorer.ista.ac.at/download/10642/10647/2022_LettersMathPhys_Henheik.pdf application/pdfno Springer Nature2022 eng mathematical physicsstatistical and nonlinear physics 0377-9017 1573-0530 2106.13780 35125630 00074493040000110.1007/s11005-021-01494-y 1121 https://research-explorer.ista.ac.at/record/19540 Henheik, S. J., Teufel, S., &#38; Wessel, T. (2022). Local stability of ground states in locally gapped and weakly interacting quantum spin systems. <i>Letters in Mathematical Physics</i>. Springer Nature. <a href="https://doi.org/10.1007/s11005-021-01494-y">https://doi.org/10.1007/s11005-021-01494-y</a> Henheik SJ, Teufel S, Wessel T. Local stability of ground states in locally gapped and weakly interacting quantum spin systems. <i>Letters in Mathematical Physics</i>. 2022;112(1). doi:<a href="https://doi.org/10.1007/s11005-021-01494-y">10.1007/s11005-021-01494-y</a> S. J. Henheik, S. Teufel, and T. Wessel, “Local stability of ground states in locally gapped and weakly interacting quantum spin systems,” <i>Letters in Mathematical Physics</i>, vol. 112, no. 1. Springer Nature, 2022. Henheik, Sven Joscha, et al. “Local Stability of Ground States in Locally Gapped and Weakly Interacting Quantum Spin Systems.” <i>Letters in Mathematical Physics</i>, vol. 112, no. 1, 9, Springer Nature, 2022, doi:<a href="https://doi.org/10.1007/s11005-021-01494-y">10.1007/s11005-021-01494-y</a>. Henheik, Sven Joscha, Stefan Teufel, and Tom Wessel. “Local Stability of Ground States in Locally Gapped and Weakly Interacting Quantum Spin Systems.” <i>Letters in Mathematical Physics</i>. Springer Nature, 2022. <a href="https://doi.org/10.1007/s11005-021-01494-y">https://doi.org/10.1007/s11005-021-01494-y</a>. Henheik SJ, Teufel S, Wessel T. 2022. Local stability of ground states in locally gapped and weakly interacting quantum spin systems. Letters in Mathematical Physics. 112(1), 9. S.J. Henheik, S. Teufel, T. Wessel, Letters in Mathematical Physics 112 (2022). 106422022-01-18T16:18:25Z2026-04-07T12:37:10Z