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：我们利用变分蒙特卡洛方法，以受限玻尔兹曼机作为试探波函数尝试，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。在基于序参量和第二Rényi熵的有限尺寸标度分析中，我们发现当衰变指数$\alpha_\mathrm{LR}$较小时，中心荷偏离1/2，而临界指数无论所考察的$\alpha_\mathrm{LR}$如何均非常接近短程（SR）伊辛值，这支持了先前提出的共形不变性破缺场景。为确定伊辛普适性和共形对称性的阈值，我们还对普适Binder比和相关函数的共形场论（CFT）描述进行了两项额外测试。结果均表明，在$\alpha_\mathrm{LR} < 2$时存在与SR伊辛类的显著偏离。然而，对$\alpha_\mathrm{LR} \ge 2$时标度化相关函数的更细致观察显示，其从$\alpha_\mathrm{LR} = 3$处已验证的CFT渐近线缓慢变化，从而提供了阈值的大致估计范围：$2 \lesssim \alpha_\mathrm{LR} < 3$。