Lie-Schwinger block-diagonalization and gapped quantum chains with unbounded interactions
Abstract
We study quantum chains whose Hamiltonians are perturbations by interactions of short range of a Hamiltonian that does not couple the degrees of freedom located at different sites of the chain and has a strictly positive energy gap above its ground-state energy. For interactions that are form-bounded w.r.t. the on-site Hamiltonian terms, we prove that the spectral gap of the perturbed Hamiltonian above its ground-state energy is bounded from below by a positive constant uniformly in the length of the chain, for small values of a coupling constant. In our proof we use a novel method introduced in [FP] and based on local Lie-Schwinger conjugations of the Hamiltonians associated with connected subsets of the chain.
Cite
@article{arxiv.1908.07450,
title = {Lie-Schwinger block-diagonalization and gapped quantum chains with unbounded interactions},
author = {S. Del Vecchio and J. Fröhlich and A. Pizzo and S. Rossi},
journal= {arXiv preprint arXiv:1908.07450},
year = {2020}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1812.02457, arXiv:1908.07486