Abstract

We analyze a variety of integration schemes for the momentum space functional renormalization group calculation with the goal of finding an optimized scheme. Using the square lattice \(t-t'\) Hubbard model as a testbed we define and benchmark the quality. Most notably we define an error estimate of the solution for the ordinary differential equation circumventing the issues introduced by the divergences at the end of the FRG flow. Using this measure to control for accuracy we find a threefold reduction in number of required integration steps achievable by choice of integrator. We herewith publish a set of recommended choices for the functional renormalization group, shown to decrease the computational cost for FRG calculations and representing a valuable basis for further investigations.

Graphic abstract

中文翻译：

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用于功能重整化组计算的更好积分器

摘要

我们分析了动量空间泛函重整化群计算的各种积分方案，目的是找到一个优化的方案。使用方格\(tt'\) Hubbard 模型作为测试平台，我们定义和基准测试质量。最值得注意的是，我们定义了常微分方程解的误差估计，以规避 FRG 流末端的分歧引入的问题。使用这种方法来控制精度，我们发现通过选择积分器可以将所需积分步骤的数量减少三倍。我们在此发布了一组功能重整化组的推荐选择，表明可以降低 FRG 计算的计算成本，并为进一步研究提供有价值的基础。

图形摘要