We study the short-imaginary-time quantum critical dynamics (SITQCD) in the $J-Q_3$ spin chain, which hosts a quasi-long-range-order phase to a valence bond solid transition. By using the scaling form of the SITQCD with a saturated ordered phase, we are able to locate the critical point at $q_{\mathrm{c}}=0.170\left(14\right)$. We also obtain the critical initial slip exponent $\theta =-0.507\left(3\right)$ and the static exponent $\beta /\nu =0.498\left(2\right)$. More strikingly, we find that the scaling dimension of the initial order parameter $x_0$ is close to zero, which suggests that the initial order parameter is a marginal operator. As a result, there is no initial increase behavior of the order parameter in the short-imaginary-time relaxation process for this model, which is very different from the relaxation dynamics in the Ising-type phase transitions. Our numerical results are realized by the projector quantum Monte Carlo algorithm.

中文翻译：

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J-Q3自旋链中的短虚时量子临界动力学

我们研究了短虚时量子临界动力学（SITQCD） $Ĵ-{问}_3$自旋链，其具有准长程相至价键固体过渡。通过使用具有饱和有序相位的SITQCD的缩放形式，我们可以将临界点定位在$q_{\mathrm{C}}=0.170（14）$。我们还获得了关键的初始滑移指数$\theta =-0.507（3）$ 和静态指数 $\beta /\nu =0.498（2）$。更惊人的是，我们发现初始阶参数的缩放比例$X_0$接近零，这表明初始订单参数是边际运算符。结果，该模型的短虚时弛豫过程中没有阶跃参数的初始增加行为，这与Ising型相变中的弛豫动力学有很大不同。我们的数值结果是通过投影机的量子蒙特卡洛算法实现的。