张量网络年龄的无偏蒙特卡罗方法
Unbiased Monte Carlo for the age of tensor networks
摘要：
介绍了一种新的无偏蒙特卡罗技术，称为张量网络蒙特卡罗（TNMC）的基础上采样所有可能的重正化（或粗粒化）的张量网络，在这种情况下，矩阵产品状态。张量网络是一种自然语言，用于表达广泛的离散物理和统计问题，例如处于热平衡的晶格上的经典和量子系统。通过同时采样与张量网络（及其重正化形式）的每个键相关的多个自由度，我们可以实现前所未有的低水平统计波动，同时平行于张量网络的令人印象深刻的精度标度，同时完全避免这些技术固有的变分偏差，即使是小键尺寸。所得到的技术本质上是一个积极的多采样技术，可以占大多数的配分函数在一个单一的样本。该方法是相当普遍的，可以与各种张量重整化技术相结合，适合于不同的几何形状和维数。
英文摘要：
A new unbiased Monte Carlo technique called Tensor Network Monte Carlo (TNMC) is introduced based on sampling all possible renormalizations (or course-grainings) of tensor networks, in this case matrix-product states. Tensor networks are a natural language for expressing a wide range of discrete physical and statistical problems, such as classical and quantum systems on a lattice at thermal equilibrium. By simultaneously sampling multiple degrees of freedom associated with each bond of the tensor network (and its renormalized form), we can achieve unprecedented low levels of statistical fluctuations which simultaneously parallel the impressive accuracy scaling of tensor networks while avoiding completely the variational bias inherent to those techniques, even with small bond dimensions. The resulting technique is essentially an aggressive multi-sampling technique that can account for the great majority of the partition function in a single sample. The method is quite general and can be combined with a variety of tensor renormalization techniques appropriate to different geometries and dimensionalities.
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。
