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

TL;DR

This study employs high-precision quantum Monte Carlo and finite-size scaling to accurately determine the quantum critical points of S=1/2 Heisenberg antiferromagnetic bilayers, confirming universality class predictions.

Contribution

It provides the most precise estimates to date of critical coupling ratios and confirms the universality class of the quantum phase transition in these systems.

Findings

Critical coupling for full bilayer: g_c=2.52181(3)

Critical coupling for incomplete bilayer: g_c=1.38882(2)

Correlation length exponent: nu=0.7106(9)

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 intra- and inter-plane couplings J and J_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_perp/J. The individual estimates of g_c are consistent provided that subleading finite-size corrections are properly taken into account. In the case of the complete bilayer, the Binder ratio leads to the most precise estimate of the critical coupling, although the subleading finite-size corrections to the stiffness are considerably smaller. For the incomplete bilayer, the subleading corrections to the stiffness are extremely small, and this quantity then gives the best estimate of the critical point. Contrary to predictions, we do not find a universal prefactor of the 1/L spin stiffness scaling at the critical point, whereas the Binder ratio is consistent with a universal value. Our results for the critical coupling ratios are g_c=2.52181(3) (full bilayer) and g_c=1.38882(2) (incomplete bilayer), which represent improvements of two orders of magnitude relative to the previous best estimates. For the correlation length exponent we obtain nu = 0.7106(9), consistent with the expected 3D Heisenberg universality class.