We study quantum chains whose Hamiltonians are perturbations by interactions of short range of a Hamiltonian consisting of a sum of on-site terms that do not couple the degrees of freedom located at different sites of the chain and have a strictly positive energy gap above their ground-state energy. For interactions that are form-bounded w.r.t. the on-site 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. Our proof is based on an extension of a novel method introduced in [FP] involving local Lie–Schwinger conjugations of the Hamiltonians associated with connected subsets of the chain.

Lie–Schwinger Block-Diagonalization and Gapped Quantum Chains with Unbounded Interactions

Del Vecchio Simone;Rossi Stefano
2021-01-01

Abstract

We study quantum chains whose Hamiltonians are perturbations by interactions of short range of a Hamiltonian consisting of a sum of on-site terms that do not couple the degrees of freedom located at different sites of the chain and have a strictly positive energy gap above their ground-state energy. For interactions that are form-bounded w.r.t. the on-site 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. Our proof is based on an extension of a novel method introduced in [FP] involving local Lie–Schwinger conjugations of the Hamiltonians associated with connected subsets of the chain.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/344066
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