High-precision finite-size scaling analysis of the quantum-critical point ofS=1∕2Heisenberg antiferromagnetic bilayers

2005/09/28 by Ling Wang, K. S. D. Beach, Anders W. Sandvik · 10 citations
Mathematics · Physics and Astronomy · #Algorithm #Computer science #Discrete mathematics #Geometry #Magnetic properties of thin films #Mathematics #Physics of Superconductivity and Magnetism #Point (geometry) #Scaling #Theoretical and Computational Physics #cond-mat.stat-mech #cond-mat.str-el

paper · pdf · doi:10.1103/physrevb.73.014431

published as Phys. Rev. B 73, 014431 (2006) · 10 pages, 10 figures

arxiv created 2005/09/28 · openalex publication_date 2006/01/27 · arxiv updated 2011/04/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We use quantum Monte Carlo (stochastic series expansion) and finite-size scaling to study the quantum critical points of two S=1∕2 Heisenberg antiferromagnets in two dimensions: a bilayer and a Kondo-lattice-like system (incomplete bilayer), each with intraplane and interplane couplings J and J_\ensuremath⊥. We discuss the ground-state finite-size scaling properties of three different quantities---the Binder moment ratio, the spin stiffness, and the long-wavelength magnetic susceptibility---which we use to extract the critical value of the coupling ratio g=J_\ensuremath⊥∕J. The individual estimates of g_c are consistent provided that subleading finite-size corrections are properly taken into account. For both models, we find that the spin stiffness has the smallest subleading finite-size corrections; in the case of the incomplete bilayer we find that the first subleading correction vanishes or is extremely small. In agreement with predictions, we find that at the critical point the Binder ratio has a universal value and the product of the spin stiffness and the long-wavelength susceptibility scales as 1∕L² with a universal prefactor. Our results for the critical coupling ratios are g_c=2.5220(1) (full bilayer) and g_c=1.3888(1) (incomplete bilayer), which represent improvements of more than an order of magnitude over the previous best estimates. For the correlation length exponent we obtain \ensuremathν=0.7106(9), consistent with the expected three-dimensional Heisenberg universality class.

Citations

• Low Temperature Behavior and Crossovers of the Square Lattice Quantum Heisenberg Antiferromagnet
• Critical exponents of the classical three-dimensional Heisenberg model: A single-cluster Monte Carlo study
• Nearly critical ground state ofLaCuO2.5
• Low Temperature Properties of the Double Layer Quantum Heisenberg Antiferromagnet -Modified Spin Wave Method-
• Quantum impurity in an antiferromagnet: Nonlinear sigma model theory
• Ground-state phase diagram of quantum Heisenberg antiferromagnets on the anisotropic dimerized square lattice
• Critical Exponents of the Quantum Phase Transition in a Planar Antiferromagnet
• Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State

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• Quantum phase transition in a Heisenberg antiferromagnet on a square lattice with strong plaquette interactions
• Coplanar order induced by emergent frustration
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• Investigation of a universal behavior between Néel temperature and staggered magnetization density for a three-dimensional quantum antiferromagnet
• Linked-cluster expansions for quantum magnets on the hypercubic lattice
• Phase transitions in spin-orbital models with spin-space anisotropies for iron pnictides: Monte Carlo simulations
• Two-particle bound states and one-particle structure factor in a Heisenberg bilayer system