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.
Frohlich, J., Pizzo, A. (2020). Lie-Schwinger block-diagonalization and gapped quantum chains. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 375(3), 2039-2069 [10.1007/s00220-019-03613-2].
Lie-Schwinger block-diagonalization and gapped quantum chains
Pizzo, A
2020-03-20
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
