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Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. I. The
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FRG 流动方程的数值流体动力学：零维 QFT 作为数值测试用例。
DOI：
10.1103/physrevd.106.065012
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发表时间：
2021
影响因子：
5
通讯作者：
D. Rischke
中科院分区：
文献类型：
--
作者：
Adrian Koenigstein;M. Steil;Nicolas Wink;E. Grossi;J. Braun;M. Buballa;D. Rischke
泛函重整化群（FRG）方法是研究各种系统的有力工具，从强相互作用理论的统计物理到引力。这种方法的实际应用依赖于所谓的流方程的推导，流方程描述了在粗粒化参数变化下量子有效作用量的变化。在目前的工作中，我们详细讨论了一种新的方法来解决这样的流动方程。这种方法依赖于这样一个事实，即RG方程可以重写，使它们表现出与流体动力学守恒定律的相似性。可以以不同的方式利用这一观察。首先，我们表明，这允许采用强大的数值技术开发的背景下，流体动力学来解决RG方程。特别是，它使我们能够可靠地对待非分析行为的出现，在RG流的有效行动，因为它是预期发生在研究，例如，自发对称破缺其次，RG方程和流体动力学之间的类比提供了机会，以获得新的见解RG流量和他们的解释一般，包括RG流量的不可逆性。我们通过将其应用于零维量子场论模型，在实践中解决了这种联系。还讨论了高维模型的推广。我们的研究结果，预计将有助于改善未来的FRG研究的量子场论在更高的维度上的定性和定量水平。
The functional renormalization group (FRG) approach is a powerful tool for studies of a large variety of systems, ranging from statistical physics over the theory of the strong interaction to gravity. The practical application of this approach relies on the derivation of so-called flow equations, which describe the change of the quantum effective action under the variation of a coarse-graining parameter. In the present work, we discuss in detail a novel approach to solve such flow equations. This approach relies on the fact that RG equations can be rewritten such that they exhibit similarities with the conservation laws of fluid dynamics. This observation can be exploited in different ways. First of all, we show that this allows to employ powerful numerical techniques developed in the context of fluid dynamics to solve RG equations. In particular, it allows us to reliably treat the emergence of nonanalytic behavior in the RG flow of the effective action as it is expected to occur in studies of, e.g., spontaneous symmetry breaking. Second, the analogy between RG equations and fluid dynamics offers the opportunity to gain novel insights into RG flows and their interpretation in general, including the irreversibility of RG flows. We work out this connection in practice by applying it to zero-dimensional quantum-field theoretical models. The generalization to higher-dimensional models is also discussed. Our findings are expected to help improving future FRG studies of quantum field theories in higher dimensions both on a qualitative and quantitative level.