论文标题
对四个玻色子重归其化组极限周期的新见解
New insights into four-boson renormalization group limit cycles
论文作者
论文摘要
使用机器学习技术，我们验证了超出统一限制的重新归一化组限制循环的出现，从三个玻色子子系统转移到整个四个玻璃系统。集中在四个相同的玻色子上，我们首先在增强的变异自动编码器集合的潜在空间内产生了合成奇异电位的种群。在引入了限制周期损失以测量给定重新归一化组流与极限周期行为的偏差之后，我们通过将精英遗传算法应用于生成的种群中最小化。观察到适量势是在反方势周围积累的，我们证明这是为了产生四个玻色子的极限周期，并且已经知道这是在三个玻色子系统中产生极限周期的。这也表明，四体项不会以领先顺序输入低能的可观察力，因为我们没有观察到任何额外的规模出现。
Using machine learning techniques, we verify that the emergence of renormalization group limit cycles beyond the unitary limit is transferred from the three-boson subsystems to the whole four-boson system. Focussing on four identical bosons, we first generate populations of synthetic singular potentials within the latent space of a boosted ensemble of variational autoencoders. After introducing the limit cycle loss for measuring the deviation of a given renormalization group flow from limit cycle behavior, we minimize it by applying an elitist genetic algorithm to the generated populations. The fittest potentials are observed to accumulate around the inverse-square potential, which we prove to generate limit cycles for four bosons and which is already known to produce limit cycles in the three-boson system. This also indicates that a four-body term does not enter low-energy observables at leading order, since we do not observe any additional scale to emerge.
