How Much Delocalisation is Needed for an Enhanced Area Law of the Entanglement Entropy?

2019/03/31 by Peter Müller, L. А. Pastur, Leonid Pastur +1 · 21 citations
Computer Science · Mathematics · Physics and Astronomy · #Bernoulli's principle #Dimension (graph theory) #Entropy (arrow of time) #Fermi Gamma-ray Space Telescope #Law #Mathematics #Physics #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Statistical physics #Thermodynamics #math-ph #math.MP #math.SP #msc:34L40 #msc:81Q10 #quant-ph

paper · pdf · doi:10.1007/s00220-019-03523-3

published in Communications in Mathematical Physics 376(1), 649-679 (Springer Science+Business Media) · 29 pages, changes in v3: correction of an error in the appendix in Lemma A.2, typos corrected

openalex created_date 2019/03/22 · openalex publication_date 2019/08/01 · arxiv created 2019/11/09 · arxiv updated 2021/03/03 · openalex updated_date 2026/08/05

Abstract

We consider the random dimer model in one space dimension with Bernoulli disorder. For sufficiently small disorder, we show that the entanglement entropy exhibits at least a logarithmically enhanced area law if the Fermi energy coincides with a critical energy of the model where the localisation length diverges.

Citations

• Colloquium: Area laws for the entanglement entropy
• Anderson localization for Bernoulli and other singular potentials
• Exponential Decay of Correlations Implies Area Law
• Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture
• Calculation of reduced density matrices from correlation functions
• Black Holes and Entropy
• Entanglement in many-body systems
• Quantum entanglement
• Dynamical Localization for the Random Dimer Model
• Localization properties of the disordered XY spin chain