Local stability of ground states in locally gapped and weakly interacting quantum spin systems

Abstract

Based on a result by Yarotsky (J. Stat. Phys. 118, 2005), we prove that localized but otherwise arbitrary perturbations of weakly interacting quantum spin systems with uniformly gapped on-site terms change the ground state of such a system only locally, even if they close the spectral gap. We call this a strong version of the local perturbations perturb locally (LPPL) principle which is known to hold for much more general gapped systems, but only for perturbations that do not close the spectral gap of the Hamiltonian. We also extend this strong LPPL-principle to Hamiltonians that have the appropriate structure of gapped on-site terms and weak interactions only locally in some region of space. While our results are technically corollaries to a theorem of Yarotsky, we expect that the paradigm of systems with a locally gapped ground state that is completely insensitive to the form of the Hamiltonian elsewhere extends to other situations and has important physical consequences.

arXiv comment9 pages, 2 figures; v1->v2: added references, v2->v3: updated references

References in corpus (10)

• Quasi-adiabatic Continuation of Quantum States: The Stability of Topological Ground State Degeneracy and Emergent Gauge Invariance
• 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
• Persistence of exponential decay and spectral gaps for interacting fermions
• Adiabatic currents for interacting electrons on a lattice
• Local Perturbations Perturb -Exponentially- Locally
• Stability of invertible, frustration-free ground states against large perturbations
• Quasi-Locality Bounds for Quantum Lattice Systems. Part II. Perturbations of Frustration-Free Spin Models with Gapped Ground States

Cited by in corpus (5)

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• Stability of thermal equilibrium in long-range quantum systems
• On adiabatic theory for extended fermionic lattice systems