Quantitative functional renormalization group description of the two-dimensional Hubbard model

RWTH Publications (RWTH Aachen)

Abstract

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 momentum dependences of the two-particle vertex, which combines a proper inclusion of the high-frequency asymptotics with the so-called truncated unity fRG for the momentum dependence. The adoption of the latter scheme requires, as an essential step, a consistent modification of the flow equation of the self-energy. We quantitatively compare our fRG results for the self-energy and momentum-dependent susceptibilities and the corresponding solution of the parquet approximation to determinant quantum Monte Carlo data, demonstrating that the fRG is remarkably accurate up to moderate interaction strengths. The presented methodological improvements illustrate how fRG flows can be brought to a quantitative level for two-dimensional problems, providing a solid basis for the application to more general systems.

Authors 8

1. Cornelia Hille

   University of Tübingen

   Affiliation as printed

   Institut für Theoretische Physik and Center for Quantum Science, Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany

2. Fabian B. Kugler

   Center for NanoScience · Munich Center for Quantum Science and Technology · Ludwig-Maximilians-Universität München

   Affiliation as printed

   Arnold Sommerfeld Center for Theoretical Physics, Center for NanoScience, and Munich Center for Quantum Science and Technology, Ludwig-Maximilians-Universität München, 80333 Munich, Germany

3. Christian Eckhardt Aachen Institute for Theoretical Solid State Physics

   TU Wien · Jülich Aachen Research Alliance · RWTH Aachen University

   Affiliation as printed

   Institute for Theoretical Solid State Physics, RWTH Aachen University, 52056 Aachen, Germany

   Institute of Solid State Physics, Vienna University of Technology, 1040 Vienna, Austria

   JARA-FIT, JARA-HPC, Jülich Aachen Research Alliance, 52425 Jülich, Germany

4. Yuan-Yao He

   William & Mary · Flatiron Institute

   Affiliation as printed

   Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA

   Department of Physics, College of William and Mary, Williamsburg, Virginia 23187, USA

5. Anna Kauch

   TU Wien

   Affiliation as printed

   Institute of Solid State Physics, Vienna University of Technology, 1040 Vienna, Austria

6. Carsten Honerkamp Aachen Institute for Theoretical Solid State Physics

   Jülich Aachen Research Alliance · RWTH Aachen University

   Affiliation as printed

   Institute for Theoretical Solid State Physics, RWTH Aachen University, 52056 Aachen, Germany

   JARA-FIT, JARA-HPC, Jülich Aachen Research Alliance, 52425 Jülich, Germany

7. A. Toschi

   TU Wien

   Affiliation as printed

   Institute of Solid State Physics, Vienna University of Technology, 1040 Vienna, Austria

8. Sabine Andergassen

   University of Tübingen

   Affiliation as printed

   Institut für Theoretische Physik and Center for Quantum Science, Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany