论文标题
有关格拉斯曼张量重归其化组的更多信息
More about the Grassmann tensor renormalization group
论文作者
论文摘要
我们以$ d $尺寸的晶格费米子的超局部相互作用（包括威尔逊费米子，交错的费米子和域壁费米子）得出了张量网络表示的一般公式。格拉曼（Grassmann）张量是通过辅助格拉曼（Grassmann）变量来确定的，这些变量在邦德自由程度中起着作用。与以前的作品相比，我们的公式不参考晶格费米子的细节，并且是通过使用给定的Dirac矩阵的奇异值分解来得出的，而无需为每个费米昂进行任何临时处理。我们在数值上测试了免费的威尔逊和交错的费米子的公式，并发现它适当地适合他们。我们还发现，与Monte Carlo方法不同，Wilson Fermions在张量重构化组方法中表现出的性能比交错的费米子更好。
We derive a general formula of the tensor network representation for $d$-dimensional lattice fermions with ultra-local interactions, including Wilson fermions, staggered fermions, and domain-wall fermions. The Grassmann tensor is concretely defined with auxiliary Grassmann variables that play a role in bond degrees of freedom. Compared to previous works, our formula does not refer to the details of lattice fermions and is derived by using the singular value decomposition for the given Dirac matrix without any ad-hoc treatment for each fermion. We numerically test our formula for free Wilson and staggered fermions and find that it properly works for them. We also find that Wilson fermions show better performance than staggered fermions in the tensor renormalization group approach, unlike the Monte Carlo method.
