Ground states in relatively bounded quantum perturbations of classical lattice systems

Abstract

We consider ground states in relatively bounded quantum perturbations of classical lattice models. We prove general results about such perturbations (existence of the spectral gap, exponential decay of truncated correlations, analyticity of the ground state), and also prove that in particular the AKLT model belongs to this class if viewed at large enough scale. This immediately implies a general perturbation theory about this model.

arXiv comment25 pages

References in corpus (3)

• Matrix-product-groundstates for one-dimensional spin-1 quantum antiferromagnets
• The spectral gap for some spin chains with discrete symmetry breaking
• Expansions for one quasiparticle states in spin 1/2 systems

Cited by in corpus (28)

• Topological quantum order: stability under local perturbations
• A short proof of stability of topological order under local perturbations
• Stability of Frustration-Free Hamiltonians
• Exact ground states and topological order in interacting Kitaev/Majorana chains
• Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems
• Quantum computation on the edge of a symmetry-protected topological order
• Quasi-Locality Bounds for Quantum Lattice Systems. Part I. Lieb-Robinson Bounds, Quasi-Local Maps, and Spectral Flow Automorphisms
• Persistence of exponential decay and spectral gaps for interacting fermions
• Quantum spin systems on infinite lattices
• On the stability of topological phases on a lattice
• Undecidability of the Spectral Gap in One Dimension
• Product Vacua and Boundary State Models in d Dimensions
• Stability of Gapped Ground State Phases of Spins and Fermions in One Dimension
• Product vacua with boundary states and the classification of gapped phases
• Recent Progress in Quantum Spin Systems
• LDPC stabilizer codes as gapped quantum phases: stability under graph-local perturbations
• Perturbation Theory for Parent Hamiltonians of Matrix Product States
• Local iterative block-diagonalization of gapped Hamiltonians: a new tool in singular perturbation theory
• Stability of invertible, frustration-free ground states against large perturbations
• Locality and nonlocality of classical restrictions of quantum spin systems with applications to quantum large deviations and entanglement
• Quasi-Locality Bounds for Quantum Lattice Systems. Part II. Perturbations of Frustration-Free Spin Models with Gapped Ground States
• Stability of ground state degeneracy to long-range interactions
• Stability of the Spectral Gap for Lattice Fermions
• Stability of the spectral gap and ground state indistinguishability for a decorated AKLT model
• The Ground State of the S=1 Antiferromagnetic Heisenberg Chain is Topologically Nontrivial if Gapped
• Mourre theory and asymptotic observables in local relativistic quantum field theory
• Lieb-Robinson bounds, Arveson spectrum and Haag-Ruelle scattering theory for gapped quantum spin systems
• Quantum Spin Systems after DLS1978