Entanglement entropy in the Lipkin-Meshkov-Glick model

2004/09/30 by José I. Latorre, J. I. Latorre, Román Orús +4 · 15 citations
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Quantum Information and Cryptography #Quantum many-body systems #cond-mat.stat-mech #hep-th #quant-ph

paper · pdf · doi:10.1103/physreva.71.064101

published as Phys. Rev. A 71, 064101 (2005) · 5 pages, 5 figures, published version

openalex publication_date 2005/06/02 · arxiv created 2005/06/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analyze the entanglement entropy in the Lipkin-Meshkov-Glick model, which describes mutually interacting spin 1/2 embedded in a magnetic field. This entropy displays a singularity at the critical point that we study as a function of the interaction anisotropy, the magnetic field, and the system size. Results emerging from our analysis are surprisingly similar to those found for the one- dimensional XY chain.

Citations

• Validity of many-body approximation methods for a solvable model
• Entanglement of Formation of an Arbitrary State of Two Qubits
• Direct equivalence between quantum phase transition phenomena in radiation-matter and magnetic systems: Scaling of entanglement
• Ground state entanglement and geometric entropy in the Kitaev model

Cited by

• Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model
• Area law and vacuum reordering in harmonic networks
• Dynamical Quantum Phase Transitions in the Dissipative Lipkin-Meshkov-Glick Model with Proposed Realization in Optical Cavity QED
• Quantum critical dynamics of a qubit coupled to an isotropic Lipkin-Meshkov-Glick bath
• Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
• A family of many-body models which are exactly solvable analytically
• Universality of the negativity in the Lipkin-Meshkov-Glick model
• Circuit QED scheme for the realization of the Lipkin-Meshkov-Glick model
• Thermodynamical Limit of the Lipkin-Meshkov-Glick Model
• Entanglement Entropy beyond the Free Case
• Evaluation of ground state entanglement in spin systems with the random phase approximation
• Scaling of the von Neumann entropy across a finite-temperature phase transition
• Block entanglement entropy of ground states with long-range magnetic order
• Frustration, Area Law, and Interference in Quantum Spin Models
• ENTANGLEMENT IN VALENCE-BOND-SOLID STATES