Exact entanglement entropy of the XYZ model and its sine-Gordon limit

2009/05/31 by Elisa Ercolessi, Stefano Evangelisti, Francesco Ravanini · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Density matrix #Entropy (arrow of time) #Generalized relative entropy #Joint quantum entropy #Logarithm #Mathematical analysis #Mathematical physics #Physics #Quantum #Quantum Information and Cryptography #Quantum discord #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Quantum relative entropy #Scaling #Sine #Statistical physics #Transfer matrix #Von Neumann entropy #cond-mat.stat-mech #hep-th #quant-ph

paper · pdf · doi:10.1016/j.physleta.2010.03.014

published as Phys.Lett.A374:2101-2105,2010 · 13 pages, 1 figure - v2: typos corrected - v3: some references and comments of sine-Gordon result added - v4: typos corrected

openalex publication_date 2010/03/11 · arxiv created 2012/10/15 · arxiv updated 2012/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We obtain the exact expression for the Von Neumann entropy for an infinite bipartition of the XYZ model, by connecting its reduced density matrix to the corner transfer matrix of the eight vertex model. Then we consider the anisotropic scaling limit of the XYZ chain that yields the 1+1 dimensional sine-Gordon model. We present the formula for the entanglement entropy of the latter, which has the structure of a dominant logarithmic term plus a constant, in agreement with what is generally expected for a massive quantum field theory.

Citations

• Universality of Entropy Scaling in One Dimensional Gapless Models
• Alan Turing: A bomba, a lógica, a matemática e a cifra
• Corner Transfer Matrix Algorithm for Classical Renormalization Group
• Entanglement in theXYspin chain
• Renyi entropy of the XY spin chain
• Form factors of branch-point twist fields in quantum integrable models and entanglement entropy
• Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture
• Entropy and Area
• Density Matrix Renormalization Group Method for 2D Classical Models
• Entanglement in many-body systems

Cited by

• Generalized isotropic Lipkin–Meshkov–Glick models: ground state entanglement and quantum entropies

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