# Matrix element interference in $N$-patch functional renormalization group

## TL;DR

This paper critically examines the limitations of the N-patch functional renormalization group method in handling matrix element interference due to momentum dependence, highlighting potential inconsistencies and proposing improvements.

## Contribution

The authors identify a key deficiency in the pFRG method regarding momentum conservation and matrix element interference, and suggest a way to enhance its accuracy.

## Key findings

- pFRG struggles with matrix element interference due to momentum dependence
- Current pFRG results may be inconsistent with weak and strong coupling limits
- Improving momentum conservation in pFRG could enhance its reliability

## Abstract

We show that the N-patch functional renormalization group (pFRG), a theoretical method commonly applied for correlated electron systems, is unable to implement consistently the matrix element interference arising from strong momentum dependence in the Bloch state contents or the interaction vertices. We show that such a deficit could lead to results incompatible with checkable limits of weak and strong coupling. We propose that the pFRG could be improved by a better account of momentum conservation.