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

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....

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Bibliographic Details
Published in:Communications in mathematical physics 2021-02, Vol.381 (3), p.1115-1152
Main Authors: Del Vecchio, S., Fröhlich, J., Pizzo, A., Rossi, S.
Format: Article
Language:English
Subjects:
Chains
Classical and Quantum Gravitation
Complex Systems
Energy gap
Mathematical and Computational Physics
Mathematical Physics
Perturbation
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary: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.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-020-03878-y