Stability of the spectral gap and ground state indistinguishability for a decorated AKLT model

Abstract

We use cluster expansions to establish local indistiguishability of the finite-volume ground states for the AKLT model on decorated hexagonal lattices with decoration parameter at least 5. Our estimates imply that the model satisfies local topological quantum order (LTQO), and so the spectral gap above the ground state is stable against local perturbations.

arXiv comment38 pages, 5 figures. v2: Updated acknowledgments section

References in corpus (37)

• Rényi Divergence and Kullback-Leibler Divergence
• Entanglement spectrum of a topological phase in one dimension
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Spectral Gap and Exponential Decay of Correlations
• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• Quasi-adiabatic Continuation of Quantum States: The Stability of Topological Ground State Degeneracy and Emergent Gauge Invariance
• Topological quantum order: stability under local perturbations
• Undecidability of the Spectral Gap (short version)
• Propagation of Correlations in Quantum Lattice Systems
• A short proof of stability of topological order under local perturbations
• Stability of Frustration-Free Hamiltonians
• Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems
• Quasi-Locality Bounds for Quantum Lattice Systems. Part I. Lieb-Robinson Bounds, Quasi-Local Maps, and Spectral Flow Automorphisms
• The adiabatic theorem and linear response theory for extended quantum systems
• Stability of local quantum dissipative systems
• Persistence of exponential decay and spectral gaps for interacting fermions
• Ground states in relatively bounded quantum perturbations of classical lattice systems
• A ${\mathbb{Z}}_2$-index of symmetry protected topological phases with time reversal symmetry for quantum spin chains
• Demonstrating the AKLT spectral gap on 2D degree-3 lattices
• Existence of a Spectral Gap in the Affleck-Kennedy-Lieb-Tasaki Model on the Hexagonal Lattice
• On the convergence of cluster expansions for polymer gases
• A class of two-dimensional AKLT models with a gap
• On the stability of charges in infinite quantum spin systems
• AKLT models on decorated square lattices are gapped
• Stability of Gapped Ground State Phases of Spins and Fermions in One Dimension
• $C^1$-classification of gapped parent Hamiltonians of quantum spin chains
• An index for two-dimensional SPT states
• Undecidability of the Spectral Gap (full version)
• Vanishing Hall conductance for commuting Hamiltonians
• Automorphic equivalence preserves the split property
• Rigorous Index Theory for One-Dimensional Interacting Topological Insulators
• Local stability of ground states in locally gapped and weakly interacting quantum spin systems
• The Asymmetric Valence-Bond-Solid States in Quantum Spin Chains: The Difference Between Odd and Even Spins
• Lie-Schwinger block-diagonalization and gapped quantum chains with unbounded interactions
• Local iterative block-diagonalization of gapped Hamiltonians: a new tool in singular perturbation theory
• Stability of invertible, frustration-free ground states against large perturbations

Cited by in corpus (1)

• A Nonvanishing Spectral Gap for AKLT Models on Generalized Decorated Graphs