论文标题
Multiloop Pseudofermion FRG的基准计算
Benchmark Calculations of Multiloop Pseudofermion fRG
论文作者
论文摘要
假柔性函数重归其化组（PFFRG）是一种计算方法，用于确定沮丧的量子磁体的零温度相图。在最近的方法学进步中，流量方程的常用katanin截断扩展到包括多旋转校正，从而捕获了三粒子顶点的其他贡献[arxiv：arxiv：2011.01268，arxiv：arxiv：2011.01269]。这种发展还刺激了PFFRG的数值实现，使人们可以以前所未有的精度跟踪伪层顶点的演变。然而，尖端的求解器的整合算法有所不同，启发式方法可以离散Matsubara频率网格等等。为了对最先进的Multiloop PFFRG代码的数值鲁棒性保持信心，我们介绍并比较了两个独立开发的算法和算法不同的求解器，用于三维晶格几何图案的海森堡模型。将立方晶格海森伯格（Anti）铁磁铁带有最接近的邻居相互作用作为通用基准模型，我们找到了两个代码以定量同意的代码，通常在数字精确的几个数量级上，均在数字上，均以旋转旋转相关函数的水平和恢复性的fermalionic vertices and Renormionic vertices for Vary Loopers vary loopersers。这些基准计算进一步证实了Multiloop PFFRG求解器的使用，以应对量子磁性的非常规形式。
The pseudofermion functional renormalization group (pffRG) is a computational method for determining zero-temperature phase diagrams of frustrated quantum magnets. In a recent methodological advance, the commonly employed Katanin truncation of the flow equations was extended to include multiloop corrections, thereby capturing additional contributions from the three-particle vertex [ arXiv:2011.01268 , arXiv:2011.01269 ]. This development has also stimulated significant progress in the numerical implementation of pffRG, allowing one to track the evolution of pseudofermion vertices under the renormalization group flow with unprecedented accuracy. However, cutting-edge solvers differ in their integration algorithms, heuristics to discretize Matsubara frequency grids, and more. To lend confidence in the numerical robustness of state-of-the-art multiloop pffRG codes, we present and compare results produced with two independently developed and algorithmically distinct solvers for Heisenberg models on three-dimensional lattice geometries. Using the cubic lattice Heisenberg (anti)ferromagnet with nearest and next-nearest neighbor interactions as a generic benchmark model, we find the two codes to quantitatively agree, often up to several orders of magnitude in digital precision, both on the level of spin-spin correlation functions and renormalized fermionic vertices for varying loop orders. These benchmark calculations further substantiate the usage of multiloop pffRG solvers to tackle unconventional forms of quantum magnetism.
