We investigate the functional renormalization group (FRG) flow of the two-particle vertex function of a model for X-ray absorption in metals. Concerning the appearance of logarithmic divergences, the model is prototypical for an important class of mostly zero- and one-dimensional systems which includes the Kondo model and the interacting one-dimensional Fermi gas. For our analysis we formulate the FRG in the framework of the real-time zero-temperature formalism, in which the model was studied before with a parquet-based approach. We establish that a reasonably crafted, purely-fermionic one-loop FRG approximation is fully equivalent on a detailed level to the leading-logarithmic parquet approximation. These two approximation schemes are thus found to just represent different perspectives on the same technical steps. This finding also reconfirms the traditional understanding of the capabilities of one-loop RG approximations for such models, which was recently put into question by an investigation of the X-ray-absorption model with multiloop FRG.
KeldyshQFT: A C++ codebase for real-frequency multiloop functional renormalization group and parquet computations of the single-impurity Anderson model
We analyze the weak-coupling instabilities that may arise when multiple high-order Van Hove points are present inside the Brillouin zone. The model we consider is inspired by twisted bilayer graphene, although the analysis should be more generally applicable. We employ a parquet renormalization group analysis to identify the leading weak-coupling instabilities, supplemented with a Ginzburg-Landau treatment to resolve any degeneracies. Hence we identify the leading instabilities that can occur from weak repulsion with the power-law divergent density of states. Five correlated phases are uncover…
Competing instabilities, orbital ordering and splitting of band degeneracies from a parquet renormalization group analysis of a 4-pocket model for iron-based superconductors: application to FeSe
利用Parquet重整化群（RG）方法研究了铁基超导体全二维四口袋三轨道低能模型中的竞争不稳定性.我们推导并分析了耦合的RG流，它描述了低能费米子之间的所有物理允许的相互作用。尽管耦合的数量是大的，我们认为，只有两个稳定的固定轨迹的RG流和一个弱不稳定的固定轨迹与一个单一的不稳定方向。每个固定的轨迹在初始系统参数的空间中具有有限的吸引域。在稳定轨道上，要么只涉及$d_{xz}$和$d_{yz}$的相互作用，要么只涉及电子袋上的$d_{xy}$轨道分量占主导地位，而在弱不稳定轨道上，涉及电子袋上的$d_{xz}$（$d_{yz}$）和$d_{xy}$轨道状态的相互作用仍然相当。沿着两个稳定的固定轨道的行为已经在前面分析过[A. V. Chubukov，M. Khodas和R.M. Fernandes，arXiv：1602.05503].在这里，我们专注于沿弱不稳定轨迹的系统行为，并将结果应用到FeSe。我们发现，基于沿这条轨迹的不稳定性分析，在降低温度时的主导不稳定性是朝向{ \it三分量} d-波轨道π阶。两个分量是空穴袋和电子袋上的$d_{xz}$和$d_{yz}$轨道上的费米子密度之差，第三个分量是两个电子袋上的$d_{xy}$轨道密度之差。我们认为，这种顺序是一致的分裂带简并，观察到在最近的光电发射数据FeSe的A。Fedorov等人[arXiv：1606.03022]。
Interplay between magnetism, superconductivity, and orbital order in a 5-pocket model for iron-based superconductors - a parquet renormalization group study
The Crossover from Ordinary to Higher-Order van Hove Singularity in a Honeycomb System: A Parquet Renormalization Group Analysis
School of Physics and Astronomy and William I. Fine Theoretical Physics Institute, University of Minnesota（明尼苏达大学物理与天文学学院及威廉·I·芬恩理论物理研究所）；National High Magnetic Field Laboratory（国家高磁场实验室）
Using a leading algorithmic implementation of the functional renormalization group (fRG) for interacting fermions on two-dimensional lattices, we provide a detailed analysis of its quantitative reliability for the Hubbard model. In particular, we show that the recently introduced multiloop extension of the fRG flow equations for the self-energy and two-particle vertex allows for a precise match with the parquet approximation also for two-dimensional lattice problems. The refinement with respect to previous fRG-based computation schemes relies on an accurate treatment of the frequency and momen…
The recently introduced single-boson exchange (SBE) decomposition of the four-point vertex of interacting fermionic many-body systems is a conceptually and computationally appealing parametrization of the vertex. It relies on the notion of reducibility of vertex diagrams with respect to the bare interaction $U$, instead of a classification based on two-particle reducibility within the widely-used parquet decomposition. Here, we re-derive the SBE decomposition in a generalized framework (suitable for extensions to, e.g., inhomogeneous systems or real-frequency treatments) following from the par…
Multiloop functional renormalization group for general models
我们提出了多回路流方程的功能重整化群（fRG）框架的四点顶点和自能，制定了一个一般的费米子多体问题。这推广了先前引入的顶点流[F. B. Kugler和J. von Delft，Phys. Rev. Lett. 120，057403（2018）]，并提供了必要的修正，以完成所有涉及截断fRG流图的衍生自能流。由于其迭代的单循环结构，多循环流非常适合于数值算法，从而能够改进许多fRG计算。我们证明了它的等价性的解决方案（一阶）镶木地板方程结合Schwinger-Dyson方程的自能。
We present a multiloop pseudofermion functional renormalization group (pffRG) approach to quantum spin systems. As a test case, we study the spin-$\tfrac{1}{2}$ Heisenberg model on the kagome lattice, a prime example of a geometrically frustrated magnet believed to host a quantum spin liquid. Our main physical result is that, at pure nearest-neighbor coupling, the system shows indications for an algebraic spin liquid through slower-than-exponential decay with distance for the static spin susceptibility, while the pseudofermion self-energy develops intriguing low-energy features. Methodological…
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 discuss how the renormalization group can be used to derive effective nuclear interactions. Starting from the model-independent low-momentum interaction V_{low k}, we successively integrate out high-lying particle and hole states from momentum shells around the Fermi surface as proposed by Shankar. The renormalization group approach allows for a systematic calculation of induced interactions and yields similar contributions to the scattering amplitude as the two-body parquet equations. We review results for the 1S0 and 3P2 superfluid pairing gaps as well as the spin dependence of effective …
We investigate several fundamental characteristics of the multiloop functional renormalization group (mfRG) flow by hands of its application to a prototypical many-electron system: the Anderson impurity model (AIM). We first analyze the convergence of the algorithm in the different parameter regions of the AIM. As no additional approximation is made, the multiloop series for the local self-energy and response functions converge perfectly to the corresponding results of the parquet approximation (PA) in the weak- to intermediate-coupling regime. Small oscillations of the mfRG solution as a func…
Anisotropic suppression of quasiparticle weight in two-dimensional electron system with partially flat Fermi surface: two-loop renormalization-group analysis
本文对具有部分平坦费米面的二维电子系统进行了双圈重整化群分析。我们发现，{ \it不考虑配对机制}，准粒子的重量是各向异性抑制由于在费米面的平坦区域的几何奇异过程。当能量标度减小时，准粒子重量在平坦区域的中心附近受到最强烈的抑制，这定性地同意通过角度分辨光电子能谱实验对欠掺杂Bi $_2$ Sr $_2$ CaCu $_2$ O $_8$提出的各向异性赝能隙行为。
Using the recently introduced adaptive density-matrix renormalization-group method, we study the many spin-spin correlations of the spin-$1/2$ antiferromagnetic Heisenberg chain with random coupling constants, namely, the mean value of the bulk and of the end-to-end correlations, the typical value of the bulk correlations, and the distribution of the bulk correlations. Our results are in striking agreement with the predictions of the strong-disorder renormalization group method. We do not find any hint of logarithmic corrections neither in the bulk average correlations, which were recently rep…
The asymptotic dynamical correlation functions in one-dimensional spin chains are described by power-laws. The corresponding exponents characterize different bulk and boundary critical behavior. We present novel results for the logarithmic contribution to the boundary correlations of an isotropic Heisenberg chain. The exponent of the logarithm, $λ=1$, is derived using a renormalization group technique. We confirm our analytical results by comparing with numerical quantum Monte Carlo data.
