多体系统变分计算的连续混合自回归网络
Continuous-mixture Autoregressive Networks for efficient variational calculation of many-body systems
摘要：
我们开发了多通道深度自回归网络，直接计算具有\emph{continuous}自旋自由度的多体系统。作为一个具体的例子，我们将二维XY模型嵌入到连续混合网络中，重新发现了周期正方形晶格上的Kosterlitz-无相变（KT）相变。自回归神经网络能够准确地检测出表征准长程序的涡旋。通过从宏观热分布中学习微观概率分布，神经网络直接计算自由能，并发现在高温区出现自由涡和反涡。作为一个更精确的评估，我们计算螺旋度模量来确定KT转变温度。虽然随着晶格尺寸的增大，训练过程变得更加耗时，但训练时间在KT转变温度附近保持不变。因此，我们开发的连续混合自回归网络可以潜在地用于研究其他具有连续自由度的多体系统。
英文摘要：
We develop deep autoregressive networks with multi channels to compute many-body systems with \emph{continuous} spin degrees of freedom directly. As a concrete example, we embed the two-dimensional XY model into the continuous-mixture networks and rediscover the Kosterlitz-Thouless (KT) phase transition on a periodic square lattice. Vortices characterizing the quasi-long range order are accurately detected by the autoregressive neural networks. By learning the microscopic probability distributions from the macroscopic thermal distribution, the neural networks compute the free energy directly and find that free vortices and anti-vortices emerge in the high-temperature regime. As a more precise evaluation, we compute the helicity modulus to determine the KT transition temperature. Although the training process becomes more time-consuming with larger lattice sizes, the training time remains unchanged around the KT transition temperature. The continuous-mixture autoregressive networks we developed thus can be potentially used to study other many-body systems with continuous degrees of freedom.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
