Local stability of ground states in locally gapped and weakly interacting quantum spin systems
Abstract
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 onsite 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 LPPLprinciple to Hamiltonians that have the appropriate structure of gapped onsite 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.
 Publication:

Letters in Mathematical Physics
 Pub Date:
 February 2022
 DOI:
 10.1007/s1100502101494y
 arXiv:
 arXiv:2106.13780
 Bibcode:
 2022LMaPh.112....9H
 Keywords:

 Quantum spin system;
 Gapped ground state;
 Local stability;
 Mathematical Physics;
 81Q15;
 81Q20;
 81V70
 EPrint:
 9 pages, 2 figures