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

TL;DR

This study uses quantum Monte Carlo simulations to accurately determine universal quantities in a 2D quantum critical system, revealing that higher order theoretical corrections may worsen agreement with numerical results.

Contribution

The paper provides precise numerical values for universal quantities in 2D quantum critical systems, highlighting discrepancies with higher order theoretical predictions and suggesting the need for refined analytic approaches.

Findings

Numerical values for $S( ext{pi,pi})/( ext{chi}_s T)$ and $c/(T ext{xi})$ are approximately 1.073 and 0.963.

Higher order theoretical contributions reduce agreement with numerical results.

Refinement of analytic calculations is needed to resolve discrepancies.

Abstract

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.