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Multiloop Functional Renormalization Group That Sums Up All Parquet Diagrams
Fabian B Kugler1, Jan von Delft1
1Physics Department, Arnold Sommerfeld Center for Theoretical Physics, and Center for NanoScience, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 Munich, Germany.
This study introduces a multiloop flow equation within the functional renormalization group (FRG) framework. This advancement improves FRG calculations for the four-point vertex and self-energy, offering more accurate results.
Area of Science:
- Condensed Matter Physics
- Quantum Field Theory
Background:
- The functional renormalization group (FRG) is a powerful tool for studying quantum systems.
- Accurate calculations of the four-point vertex are crucial for understanding many-body phenomena.
Purpose of the Study:
- To develop an improved multiloop flow equation for the four-point vertex in the FRG framework.
- To enhance the accuracy of FRG computations for the four-point vertex and self-energy.
Main Methods:
- The study presents a multiloop flow equation derived from successive one-loop calculations.
- This method sums all parquet diagrams to arbitrary order.
- The approach is demonstrated using the x-ray-edge singularity as a test case.
Main Results:
- The multiloop flow equation offers substantial improvements for FRG computations.
- Solving the multiloop FRG flow is shown to be equivalent to solving the first-order parquet equations.
- Numerical results illustrate the effectiveness of the method.
Conclusions:
- The developed multiloop flow equation provides a significant advancement in FRG calculations.
- This method enhances the accuracy of the four-point vertex and self-energy calculations.
- The equivalence to parquet equations offers a new perspective and validation.
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