Lie-Schwinger block-diagonalization and gapped quantum chains with unbounded interactions
arXiv:1908.07450 · doi:10.1007/s00220-020-03878-y
Abstract
We study 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. In our proof we use a novel method introduced in [FP] and based on local Lie-Schwinger conjugations of the Hamiltonians associated with connected subsets of the chain.
arXiv commentarXiv admin note: substantial text overlap with arXiv:1812.02457, arXiv:1908.07486
References in corpus (11)
- On Many-Body Localization for Quantum Spin Chains
- Topological quantum order: stability under local perturbations
- A short proof of stability of topological order under local perturbations
- Stability of Frustration-Free Hamiltonians
- Persistence of exponential decay and spectral gaps for interacting fermions
- On gapped phases with a continuous symmetry and boundary operators
- Multi-Scale Jacobi Method for Anderson Localization
- Effective interactions due to quantum fluctuations
- Mott transition in lattice boson models
- Stability of Gapped Ground State Phases of Spins and Fermions in One Dimension
- An exponentially local spectral flow for possibly non-self-adjoint perturbations of non-interacting quantum spins, inspired by KAM theory
Cited by in corpus (4)
- Random translation-invariant Hamiltonians and their spectral gaps
- Local iterative block-diagonalization of gapped Hamiltonians: a new tool in singular perturbation theory
- Quasi-Locality Bounds for Quantum Lattice Systems. Part II. Perturbations of Frustration-Free Spin Models with Gapped Ground States
- Stability of the spectral gap and ground state indistinguishability for a decorated AKLT model