Entanglement in theXYspin chain

2004/09/30 by A. R. Its, B. -Q. Jin, B-Q Jin +1 · 12 citations
Computer Science · Physics and Astronomy · #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum many-body systems #cond-mat.stat-mech #nlin.SI #quant-ph

paper · pdf · doi:10.1088/0305-4470/38/13/011

published as Journal Phys. A: Math. Gen. vol 38, pages 2975-2990, 2005 · 8 pages and 2 figures

arxiv created 2004/10/23 · openalex publication_date 2005/03/15 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We consider the ground state of the XY model on an infinite chain at zero temperature. Following Bennett, Bernstein, Popescu, and Schumacher we use entropy of a sub-system as a measure of entanglement. Vidal, Latorre, Rico and Kitaev conjectured that von Neumann entropy of a large block of neighboring spins approaches a constant as the size of the block increases. We evaluated this limiting entropy as a function of anisotropy and transverse magnetic field. We used the methods based on integrable Fredholm operators and Riemann-Hilbert problem. The entropy is singular at phase transitions.

Citations

• Quantum Inverse Scattering Method and Correlation Functions
• Universality of Entropy Scaling in One Dimensional Gapless Models
• Diverging Entanglement Length in Gapped Quantum Spin Systems
• Universality of entanglement and quantum-computation complexity
• Two soluble models of an antiferromagnetic chain
• Fredholm determinants, differential equations and matrix models

Cited by

• Bound entanglement in the XY model
• ENTANGLEMENT IN VALENCE-BOND-SOLID STATES
• Ellipses of constant entropy in theXYspin chain
• Renyi entropy of the XY spin chain
• Exact entanglement entropy of the XYZ model and its sine-Gordon limit
• Local entanglement and quantum phase transition in spin models
• Local Convertibility and the Quantum Simulation of Edge States in Many-Body Systems
• Dynamics of a quantum phase transition and relaxation to a steady state
• Class of Quantum Many-Body States That Can Be Efficiently Simulated
• Generalized isotropic Lipkin–Meshkov–Glick models: ground state entanglement and quantum entropies
• Generalized entropy of the Heisenberg spin chain
• Vladimir Korepin [wikipedia]