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$2\times2$, C$2\times4$ and C$4\times4$. 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$2\times2$ 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$2\times4$ and C$4\times4$ 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.