BosonFlow: A C++ codebase for dynamic fRG and single-boson exchange in correlated fermion systems
Ruhr-University Bochum（波鸿鲁尔大学）；Max-Planck-Institut für Festkörperforschung（马克斯·普朗克固体研究所）；Vienna University of Technology（维也纳工业大学）；Universität Tübingen（蒂宾根大学）
We present a unified C++ implementation of the functional renormalization group and the parquet equations within the single-boson exchange formalism for several paradigmatic tight-binding and impurity models at equilibrium. The implementation computes the full dynamic vertex and self-energies, with momentum dependence treated using a truncated unity framework. We implement multiple self-energy flow equations, cutoff schemes, and extensions ranging from the dynamical functional renormalization group to multiloop flow equations that incorporate cutoffs in both the propagator and the interaction. The codebase serves as a reference for recent developments in the fRG and parquet methods for correlated electron systems and provides a flexible foundation for developing new many-body approaches and extensions.
KeldyshQFT: A C++ codebase for real-frequency multiloop functional renormalization group and parquet computations of the single-impurity Anderson model
Functional renormalization group without functional integrals: implementing Hilbert space projections for strongly correlated electrons via Hubbard X-operators
Although the functional renormalization group (fRG) is by now a well-established method for investigating correlated electron systems, it is still undergoing significant technical and conceptual improvements. In particular, the motivation to optimally exploit the parallelism of modern computing platforms has recently led to the development of the "truncated-unity" functional renormalization group (TU-fRG). Here, we review this fRG variant, and we provide its extension to multiband systems with spin-orbit coupling. Furthermore, we discuss some aspects of the implementation and outline opportuni…
The conceptual framework provided by the functional Renormalization Group (fRG) has become a formidable tool to study correlated electron systems on lattices which, in turn, provided great insights to our understanding of complex many-body phenomena, such as high- temperature superconductivity or topological states of matter. In this work we present one of the latest realizations of fRG which makes use of an adaptive numerical quadrature scheme specifically tailored to the described fRG scheme. The final result is an increase in performance thanks to improved parallelism and scalability.
Renormalization group methods are well-established tools for the (numerical) investigation of the low-energy properties of correlated quantum many-body systems, allowing to capture their scale-dependent nature. The functional renormalization group (FRG) allows to continuously evolve a microscopic model action to an effective low-energy action as a function of decreasing energy scales via an exact functional flow equation, which is then approximated by some truncation scheme to facilitate computation. Here, we report on our transcription of a recently developed multiloop truncation approach for…
We perform a data-driven dimensionality reduction of the scale-dependent 4-point vertex function characterizing the functional Renormalization Group (fRG) flow for the widely studied two-dimensional $t - t'$ Hubbard model on the square lattice. We demonstrate that a deep learning architecture based on a Neural Ordinary Differential Equation solver in a low-dimensional latent space efficiently learns the fRG dynamics that delineates the various magnetic and $d$-wave superconducting regimes of the Hubbard model. We further present a Dynamic Mode Decomposition analysis that confirms that a small …
We propose new approach for treatment of local and non-local interactions in correlated electronic systems, which uses self-energy and the two-particle irreducible vertices, obtained from (extended) dynamical mean-field theory, as an input of two-particle irreducible functional renormalization-group (2PI-fRG) approach. Using 2PI-fRG approach allows us to treat both, local and non-local interactions. In case of purely local interaction the corresponding equations have similar (although not identical) structure to the earlier developed DMF$^2$RG approach. In a simplest truncation, neglecting sca…
Functional renormalization-group approaches, one-particle (ir)reducible with respect to local Green functions, using the dynamical mean-field theory as a starting point
我们考虑相关电子系统的泛函重整化群流的公式，以动力学平均场论为出发点。我们将相应的重整化群格式分为忽略单粒子不可约（相对于局部格林函数）的六点顶点和忽略单粒子可约的六点顶点两类。前一类由最近引入的DMF $^{2}$ RG方法[Phys. Rev. Lett. 112，196402（2014）]，而且还通过生成泛函的单粒子不可约（相对于局部格林函数，1 PI-LGF）表示的尺度相关推广[Phys.Rev.B88，115112（2013）]。第二类由双费米子（DF）方法内的fRG流表示[Phys.Rev.B77，033101（2008）; ArXiv 1411.1342]。我们比较配方的fRG方法在这些情况下，并建议其进一步的应用研究二维系统内的哈伯德模型。
Spontaneous current orders due to odd-parity order parameters attract increasing attention in various strongly correlated metals. Here, we discover a novel spin-fluctuation-driven charge loop current (cLC) mechanism based on the functional renormalization group (fRG) theory. The present mechanism leads to the ferro-cLC order in a simple frustrated chain Hubbard model. The cLC appears between the antiferromagnetic and $d$-wave superconducting ($d$SC) phases. While the microscopic origin of the cLC has a close similarity to that of the $d$SC, the cLC transition temperature $T_{\rm cLC}$ can be h…
