We investigate quantum phase transitions in the transverse field Ising chain with algebraically decaying long-range antiferromagnetic interactions by using the variational Monte Carlo method with the restricted Boltzmann machine being employed as a trial wave function ansatz. In the finite-size scaling analysis with the order parameter and the second R\'enyi entropy, we find that the central charge deviates from 1/2 at a small decay exponent $\alpha_\mathrm{LR}$ in contrast to the critical exponents staying very close to the short-range (SR) Ising values regardless of $\alpha_\mathrm{LR}$ examined, supporting the previously proposed scenario of conformal invariance breakdown. To identify the threshold of the Ising universality and the conformal symmetry, we perform two additional tests for the universal Binder ratio and the conformal field theory (CFT) description of the correlation function. It turns out that both indicate a noticeable deviation from the SR Ising class at $\alpha_\mathrm{LR} < 2$. However, a closer look at the scaled correlation function for $\alpha_\mathrm{LR} \ge 2$ shows a gradual change from the asymptotic line of the CFT verified at $\alpha_\mathrm{LR} = 3$, providing a rough estimate of the threshold being in the range of $2 \lesssim \alpha_\mathrm{LR} < 3$.

翻译：我们采用受限玻尔兹曼机作为试探波函数变分蒙特卡罗方法，研究了具有代数衰减长程反铁磁相互作用的横场伊辛链中的量子相变。通过基于序参量和第二Rényi熵的有限尺寸标度分析，我们发现当衰减指数$\alpha_\mathrm{LR}$较小时，中心荷偏离1/2，而临界指数则始终非常接近短程伊辛模型的数值——无论所考察的$\alpha_\mathrm{LR}$值如何——这支持了此前提出的共形对称性破缺假说。为确定伊辛普适性与共形对称性的阈值，我们进一步进行了两项检验：普适Binder比率以及关联函数的共形场论描述。结果表明，当$\alpha_\mathrm{LR} < 2$时，两者均明显偏离短程伊辛类行为。然而，对$\alpha_\mathrm{LR} \ge 2$时的标度关联函数进行更细致的观察，发现其从$\alpha_\mathrm{LR} = 3$处验证的共形场论渐近线逐渐偏离，据此粗略估计阈值位于$2 \lesssim \alpha_\mathrm{LR} < 3$范围内。