Lie-Schwinger block-diagonalization and gapped quantum chains
Mathematical Physics
2019-02-28 v2 math.MP
Abstract
We study quantum chains whose Hamiltonians are perturbations by bounded 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. We prove that, for small values of a coupling constant, 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. In our proof we use a novel method based on local Lie-Schwinger conjugations of the Hamiltonians associated with connected subsets of the chain.
Cite
@article{arxiv.1812.02457,
title = {Lie-Schwinger block-diagonalization and gapped quantum chains},
author = {Juerg Froehlich and Alessandro Pizzo},
journal= {arXiv preprint arXiv:1812.02457},
year = {2019}
}