A Monte Carlo examination for the numerical values of universal quantities in spatial dimension two

By simulating a two-dimensional (2D) dimerized spin-1/2 antiferromagnet with the quantum Monte Carlo method, the numerical values of two universal quantities associated with the quantum critical regime (QCR), namely $S(\pi,\pi)/\left(\chi_s T\right)$ and $c/\left(T\xi\right)$, are determined. Here $S(\pi,\pi)$, $\chi_s$, $c$, $\xi,$ and $T$ are the staggered structure factor, the staggered susceptibility, the spin-wave velocity, the correlation length, and the temperature, respectively. For other QCR universal quantities, such as the Wilson ratio $W$ and $\chi_u c^2/T$ ($\chi_u$ is the uniform susceptibility), it is shown that the addition of higher order theoretical contribution makes the agreement between the numerical and the analytic results worse. We find that the same scenario applies to $S(\pi,\pi)/\left(\chi_s T\right)$ and $c/\left(T\xi\right)$ as well. Specifically, our calculations lead to $S(\pi,\pi)/\left(\chi_s T\right)\sim 1.073$ and $c/\left(T\xi\right)\sim 0.963$ which are in better consistence with the leading theoretical predictions than those with the next-to-leading order terms. The presented outcome here as well as those in some relevant literature suggest that it is desirable to conduct a refinement of the analytic calculation to resolve the puzzle of why the inclusion of higher order terms leads to less accurate predictions for these universal quantities.