TU$^2$FRG -- a scalable approach for truncated unity functional renormalization group in generic fermionic models

TL;DR

This paper introduces TU$^2$FRG, a novel truncated unity functional renormalization group method that enhances scalability for large and symmetry-broken fermionic models, bridging real and momentum space approaches.

Contribution

The paper develops TU$^2$FRG, a unified formalism combining real and momentum space truncated unity to improve efficiency in large or symmetry-broken fermionic systems.

Findings

Significantly improved scaling over conventional TUFRG.

Effective in large unit-cell and symmetry-broken models.

Unifies real and momentum space approaches.

Abstract

Describing the emergence of phases of condensed matter is one of the central challenges in physics. For this purpose many numerical and analytical methods have been developed, each with their own strengths and limitations. The functional renormalization group is one of these methods bridging between efficiency and accuracy. In this paper we derive a new truncated unity (TU) approach unifying real- and momentum space TU, called TU$^2$FRG. This formalism significantly improves the scaling compared to conventional momentum (TU)FRG when applied to large unit-cell models and models where the translational symmetry is broken.