Entanglement negativity in the critical Ising chain

2013/02/05 by Pasquale Calabrese, Luca Tagliacozzo, Erik Tonni
Computer Science · Mathematics · Physics and Astronomy · Psychology · #Chain (unit) #Cognitive psychology #Ising model #Mathematics #Negativity effect #Opinion Dynamics and Social Influence #Physics #Psychology #Quantum #Quantum Computing Algorithms and Architecture #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Statistical physics #cond-mat.stat-mech #hep-th #quant-ph

paper · pdf · doi:10.1088/1742-5468/2013/05/p05002

published as J. Stat. Mech. (2013) P05002 · 31 pages, 14 figures

arxiv created 2013/02/05 · openalex publication_date 2013/05/07 · arxiv updated 2015/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study the scaling of the traces of the integer powers of the partially transposed reduced density matrix Tr(ρT2A) n and of the entanglement negativity for two spin blocks as function of their length and separation in the critical Ising chain. For two adjacent blocks, we show that tensor network calculations agree with universal conformal field theory (CFT) predictions. In the case of two disjoint blocks the CFT predictions are recovered only after taking into account the finite size corrections induced by the finite length of the blocks. ar X iv

Citations

• Colloquium: Area laws for the entanglement entropy
• Entanglement Negativity in Quantum Field Theory
• Mixed-State Entanglement and Distillation: Is there a “Bound” Entanglement in Nature?
• Universality of the negativity in the Lipkin-Meshkov-Glick model
• Homogeneous binary trees as ground states of quantum critical Hamiltonians
• Form factors of branch-point twist fields in quantum integrable models and entanglement entropy
• Separability Criterion for Density Matrices
• Holographic entanglement entropy: near horizon geometry and disconnected regions
• Entanglement Probe of Two-Impurity Kondo Physics in a Spin Chain
• Concatenated tensor network states
• Entanglement spectrum in one-dimensional systems
• Rényi entropy and parity oscillations of anisotropic spin-sHeisenberg chains in a magnetic field
• Inseparability Criterion for Continuous Variable Systems
• Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence
• Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
• Entanglement entropy and twist fields
• Entanglement entropy of two disjoint blocks in critical Ising models
• Peres-Horodecki Separability Criterion for Continuous Variable Systems
• Entanglement in many-body systems
• Conformal Field Theory