Criticality and scaling corrections for two-dimensional Heisenberg models in plaquette patterns with strong and weak couplings

Abstract

We use the stochastic series expansion quantum Monte Carlo method to study the Heisenberg models on the square lattice with strong and weak couplings in the form of three different plaquette arrangements known as checkerboard models C$2\times 2$, C$2\times 4$ and C$4\times 4$. The $a\times b$ here stands for the shape of plaquette consisting with spins connected by strong couplings. Through detailed analysis of finite-size scaling study, the critical point of C$2\times 2$ model is improved as $g_c=0.548524(3)$ compared with previous studies with $g$ to be the ratio of weak and strong couplings in the models. For C$2\times 4$ and C$4\times 4$ we give $g_c=0.456978(2)$ and $0.314451(3)$. We also study the critical exponents $\nu$, $\eta$, and the universal property of Binder ratio to give further evidence that all quantum phase transitions in these three models are in the three-dimensional O(3) universality class. Furthermore, our fitting results show the importance of effective corrections in the scaling study of these models.

arXiv comment8 pages,6 figures

References in corpus (33)

• Quantum phase transitions
• Bose-Einstein Condensation in Magnetic Insulators
• Critical exponents and equation of state of the three-dimensional Heisenberg universality class
• Quantum magnetism and criticality
• Quantum criticality with two length scales
• Plaquette valence bond solid in the frustrated Heisenberg quantum antiferromagnet on the square lattice
• Tensor network study of the Shastry-Sutherland model in zero magnetic field
• Ground-State Phase Diagram of Quantum Heisenberg Antiferromagnets on the Anisotropic Dimerized Square Lattice
• High-precision finite-size scaling analysis of the quantum-critical point of S=1/2 Heisenberg antiferromagnetic bilayers
• From incommensurate to dispersive spin-fluctuations: The high-energy inelastic spectrum in superconducting YBa2Cu3O6.5
• Observation of a 4-spin Plaquette Singlet State in the Shastry-Sutherland compound SrCu2(BO3)2
• Exploring frustrated spin-systems using Projected Entangled Pair States (PEPS)
• Eliminating leading corrections to scaling in the 3-dimensional O(N)-symmetric phi^4 model: N=3 and 4
• Phase Diagram of the quadrumerized Shastry-Sutherland Model
• Evidence of Unconventional Universality Class in a Two-Dimensional Dimerized Quantum Heisenberg Model
• Critical exponents of the quantum phase transition in a planar antiferromagnet
• Comprehensive quantum Monte Carlo study of the quantum critical points in planar dimerized/quadrumerized Heisenberg models
• Symmetry enhanced first-order phase transition in a two-dimensional quantum magnet
• The plaquette phase of the square lattice quantum dimer model
• Anomalous quantum-critical scaling corrections in two-dimensional antiferromagnets
• The critical Binder cumulant in a two--dimensional anisotropic Ising model with competing interaction
• Critical Binder cumulant for isotropic Ising models on square and triangular lattices
• Two-particle decay and quantum criticality in dimerized antiferromagnets
• Velocity of excitations in ordered, disordered and critical antiferromagnets
• Quantum Phase Transition in a Heisenberg Antiferromagnet on a Square Lattice with Strong Plaquette Interactions
• Solving the puzzle of an unconventional phase transition for a 2d dimerized quantum Heisenberg model
• Quantum phase transitions in disordered dimerized quantum spin models and the Harris criterion
• Monte Carlo simulation with aspect ratio optimization: Anomalous anisotropic scaling in dimerized antiferromagnet
• Two-Dimensional Quantum Spin Systems with Ladder and Plaquette Structure
• Spin excitation spectra of the two dimensional $S=1/2$ Heisenberg model with a checkerboard structure
• Equivalent-neighbor Potts models in two dimensions
• The effects of disorder in dimerized quantum magnets in mean field approximations
• Typicality at quantum-critical points

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