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 $2 \lesssim \alpha_\mathrm{LR} < 3$.

我们使用变分蒙特卡罗方法，采用 Restricted Boltzmann 机器作为试探波函数的假设，研究具有代数衰减长程反铁磁相互作用的横向场 Ising 链中的量子相变。通过有限尺度扩展分析，利用序参量和第二 Rényi 熵，我们发现在小的衰减指数 α_LR 情况下，中心荷与 1/2 偏离，与短程 Ising 值非常接近的临界指数不同，支持先前提出的共形不变性破缺的情景。为了确定 Ising 普适性和共形对称性的临界点，我们对普适 Binder 比和相关函数的共形场论（CFT）描述进行了两个额外的测试。结果表明，在 α_LR <2 的情况下，两者都显示出明显偏离短程 Ising 类的现象。然而，对于 α_LR> = 2 的情况，对缩放相关函数进行仔细观察显示出从在 α_LR = 3 处验证的 CFT 的渐变变化，为临界点提供了一个大致的估计范围：2 ≤ α_LR < 3。