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

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 ${J}_{\ensuremath{\perp}}$. 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 $g={J}_{\ensuremath{\perp}}∕J$. 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 $1∕{L}^{2}$ 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 $\ensuremath{\nu}=0.7106(9)$, consistent with the expected three-dimensional Heisenberg universality class.