Entanglement in a second-order quantum phase transition

2003/05/31 by J. Vidal, Julien Vidal, Guillaume Palacios +3 · 9 citations
Computer Science · Mathematics · Physics and Astronomy · #Concurrence #Cusp (singularity) #Ground state #Lambda #Mathematics #Order (exchange) #Phase transition #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum critical point #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Quantum phase transition #Singularity #Spin (aerodynamics) #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1103/physreva.69.022107

published as Phys. Rev. A 69, 022107 (2004) · 4 pages, 4 EPS figures, minor corrections added and title changed

arxiv created 2003/12/02 · openalex publication_date 2004/02/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We consider a system of mutually interacting spins 1/2 embedded in a transverse magnetic field which undergoes a second-order quantum phase transition. We analyze the entanglement properties and the spin squeezing of the ground state and show that, contrarily to the one-dimensional case, a cusplike singularity appears at the critical point \ensuremathλ_c in the thermodynamical limit. We also show that there exists a value \ensuremathλ₀>~\ensuremathλ_c above which the ground state is not spin squeezed despite a nonvanishing concurrence.

Citations

• Validity of many-body approximation methods for a solvable model
• Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
• Entanglement of Formation of an Arbitrary State of Two Qubits
• Characterizing the entanglement of symmetric many-particle spin-12systems
• Squeezed spin states

Cited by

• Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
• Entanglement in a first-order quantum phase transition
• Dissipative Dicke model with nonlinear atom–photon interaction
• Thermal entanglement of spins in mean-field clusters
• Dynamics of entanglement of bosonic modes on symmetric graphs
• On the thermodynamic limit of the Lipkin model
• Quasiprobability distribution functions for finite-dimensional discrete phase spaces: Spin-tunneling effects in a toy model
• Quantum coherence and uncertainty in the anisotropic XY chain
• Reduced fidelity susceptibility and its finite-size scaling behaviors in the Lipkin-Meshkov-Glick model