Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model

2004/08/31 by S. Dusuel, Sébastien Dusuel, J. Vidal +1 · 7 citations
Computer Science · Mathematics · Physics and Astronomy · #Boson #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Critical exponent #Ground state #Mathematical physics #Mathematics #Phase transition #Physics #Quantum #Quantum Information and Cryptography #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Scaling #Spin (aerodynamics) #Statistical physics #Transformation (genetics) #Unitary transformation #cond-mat.stat-mech #nucl-th #quant-ph

paper · pdf · doi:10.1103/physrevlett.93.237204

published as Phys. Rev. Lett. 93, 237204 (2004) · 4 pages, published version

arxiv created 2004/12/01 · openalex publication_date 2004/12/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study the ground state properties of the critical Lipkin-Meshkov-Glick model. Using the Holstein-Primakoff boson representation, and the continuous unitary transformation technique, we compute explicitly the finite-size scaling exponents for the energy gap, the ground state energy, the magnetization, and the spin-spin correlation functions. Finally, we discuss the behavior of the two-spin entanglement in the vicinity of the phase transition.

Citations

• Validity of many-body approximation methods for a solvable model
• Entanglement of Formation of an Arbitrary State of Two Qubits
• Entanglement in a first-order quantum phase transition
• Entanglement in a second-order quantum phase transition
• Field Dependence of the Intrinsic Domain Magnetization of a Ferromagnet
• Flow‐equations for Hamiltonians

Cited by

• Finite-size scaling exponents in the interacting boson model
• Thermal entanglement of spins in mean-field clusters
• On the thermodynamic limit of the Lipkin model
• Positive quantum Lyapunov exponents in experimental systems with a regular classical limit
• Ultrafast critical ground state preparation via bang–bang protocols
• Faster State Preparation across Quantum Phase Transition Assisted by Reinforcement Learning
• Effects of dynamical paths on the energy gap and the corrections to the free energy in path integrals of mean-field quantum spin systems
• Scalar two-level boson model to study the interacting boson model phase diagram in the Casten triangle