Local Lie-Schwinger conjugations and gapped quantum chainsProf. Alessandro Pizzo
26-11-2019 - 14:30 Largo San Leonardo Murialdo,1 - Pal.C - Aula 311
We consider 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. Under the same hypothesis, we prove that the ground state energy is analytic for values of the coupling constant in a fixed interval, uniformly in the length of the chain. |