2018/12/06 by Froehlich, Juerg, Pizzo, Alessandro · 1 citation
#FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1812.02457
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.