We report a quantum Monte Carlo study of the phase transition between antiferromagnetic and valence-bond solid ground states in the square-lattice $S=1/2$ $J$-$Q$ model. The critical correlation function of the $Q$ terms gives a scaling dimension corresponding to the value $\nu = 0.455 \pm 0.002$ of the correlation-length exponent. This value agrees with previous (less precise) results from conventional methods, e.g., finite-size scaling of the near-critical order parameters. We also study the $Q$-derivatives of the Binder cumulants of the order parameters for $L^2$ lattices with $L$ up to $448$. The slope grows as $L^{1/\nu}$ with a value of $\nu$ consistent with the scaling dimension of the $Q$ term. There are no indications of runaway flow to a first-order phase transition. The mutually consistent estimates of $\nu$ provide compelling support for a continuous deconfined quantum-critical point.

中文翻译：

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去限制量子临界点处的一致标度指数

我们报告了方格 $S=1/2$$J$-$Q$ 模型中反铁磁和价键固体基态之间相变的量子蒙特卡罗研究。$Q$ 项的临界相关函数给出了对应于相关长度指数的值 $\nu = 0.455 \pm 0.002$ 的缩放维度。该值与来自传统方法的先前（不太精确）结果一致，例如，近临界阶参数的有限尺寸缩放。我们还研究了 $L^2$ 格的阶参数的 Binder 累积量的 $Q$ 导数，其中 $L$ 高达 $448$。斜率随着 $L^{1/\nu}$ 增长，$\nu$ 的值与 $Q$ 项的缩放维度一致。没有迹象表明失控流动到一阶相变。