2005/01/31 by Román Orús, Roman Orus · 44 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Bipartite graph #Combinatorics #Conformal map #Geometry #Majorization #Mathematical analysis #Mathematical physics #Mathematics #Monotonic function #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Renormalization group #Theoretical physics #cond-mat.other #hep-th #quant-ph
paper · pdf · doi:10.1103/physreva.71.052327
published in Physical Review A 71(5) (American Physical Society) · 8 pages, 1 figure, corrected an error in the theorems from sec.III and IV
openalex publication_date 2005/05/25 · arxiv created 2005/12/15 · arxiv updated 2014/11/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Motivated by the idea of entanglement loss along renormalization group flows, analytical majorization relations are proven for the ground state of (1+1)-dimensional conformal field theories. For any of these theories, majorization is proven to hold in the spectrum of the reduced density matrices in a bipartite system when changing the size L of one of the subsystems. Continuous majorization along uniparametric flows is also proven as long as part of the conformal structure is preserved under the deformation and some monotonicity conditions hold as well. As particular examples of our derivations, we study the cases of the XX, Heisenberg, and XY quantum spin chains. Our results provide in a rigorous way explicit proofs for all the majorization conjectures raised by Latorre, L"utken, Rico, Vidal, and Kitaev in previous papers on quantum spin chains.