Stability of the Area Law for the Entropy of Entanglement

Abstract

Recent results on the stability of the spectral gap under general perturbations for frustration-free Hamiltonians, have motivated the following question: Does the entanglement entropy of quantum states that are connected to states satisfying an area law along gapped Hamiltonian paths, also satisfy an area law? We answer this question in the affirmative, combining recent advances in quasi-adiabatic evolution and Lieb-Robinson bounds with ideas from the proof of the 1D area law.

arXiv comment8 pages, extended introduction and updated references

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Cited by in corpus (9)

• Non-local propagation of correlations in long-range interacting quantum systems
• Renormalization group constructions of topological quantum liquids and beyond
• Lieb-Robinson bounds and the simulation of time evolution of local observables in lattice systems
• Entanglement and tensor network states
• On gapped phases with a continuous symmetry and boundary operators
• Mutual information area laws for thermal free fermions
• Thermal Area Law for Lattice Bosons
• Entanglement subvolume law for 2D frustration-free spin systems
• Area law for steady states of detailed-balance local Lindbladians