论文标题
计算二维$ ϕ^4 $理论的重新归一化组流量
Computing the renormalization group flow of two-dimensional $ϕ^4$ theory with tensor networks
论文作者
论文摘要
我们研究了$ ϕ^4 $理论在两个维度上的重新归一化组流量。将空间正规化为细粒晶格，并以受控的方式离散标量场，我们将理论的分区函数重写为张量网络。结合局部截断和标准的粗晶节方案，我们获得了该理论作为张量空间中图作为图的重新归一化群。除了定性的见解外，我们还验证了临界值的缩放维度，并推断临界$ f _ {\ rm c} =λ/μ^2 $ to Continuum以找到$ f^{\ rm cont。} _ {\ rm c} = 11.0861（90）$，以便于找到$ f^{\ rm cont。} _ {\ rm cont。} _ {\ rm cont。
We study the renormalization group flow of $ϕ^4$ theory in two dimensions. Regularizing space into a fine-grained lattice and discretizing the scalar field in a controlled way, we rewrite the partition function of the theory as a tensor network. Combining local truncations and a standard coarse-graining scheme, we obtain the renormalization group flow of the theory as a map in a space of tensors. Aside from qualitative insights, we verify the scaling dimensions at criticality and extrapolate the critical coupling constant $f_{\rm c} = λ/ μ^2$ to the continuum to find $f^{\rm cont.}_{\rm c} = 11.0861(90)$, which favorably compares with alternative methods.
