2011/03/31 by Michael P. Zaletel, Jens H. Bardarson, Joel E. Moore · 87 citations
Mathematics · Physics and Astronomy · #Entropy (arrow of time) #Logarithm #Mathematical analysis #Mathematics #Model Reduction and Neural Networks #Opinion Dynamics and Social Influence #Physics #Quantum #Quantum discord #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Quantum mutual information #Spin (aerodynamics) #Statistical physics #Thermodynamics #cond-mat.str-el
paper · pdf · doi:10.1103/physrevlett.107.020402
published in Physical Review Letters 107(2), 020402 (American Physical Society) · 4 pages and 4 page appendix, 4 figures
arxiv created 2011/05/26 · openalex publication_date 2011/07/05 · arxiv updated 2017/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Universal logarithmic terms in the entanglement entropy appear at quantum critical points (QCPs) in one dimension (1D) and have been predicted in 2D at QCPs described by 2D conformal field theories. The entanglement entropy in a strip geometry at such QCPs can be obtained via the "Shannon entropy" of a 1D spin chain with open boundary conditions. The Shannon entropy of the XXZ chain is found to have a logarithmic term that implies, for the QCP of the square-lattice quantum dimer model, a logarithm with universal coefficient ±0.25. However, the logarithm in the Shannon entropy of the transverse-field Ising model, which corresponds to entanglement in the 2D Ising conformal QCP, is found to have a singular dependence on the replica or Rényi index resulting from flows to different boundary conditions at the entanglement cut.