Functional renormalization of spinless triangular-lattice fermions: $N$-patch vs. truncated-unity scheme

TL;DR

This paper investigates the competing electronic orders in a triangular-lattice Hubbard model with spinless fermions, using functional renormalization group methods to compare two momentum discretization schemes and explore various interaction-driven instabilities.

Contribution

It introduces a comparative analysis of N-patch and truncated-unity schemes in functional renormalization group calculations for spinless fermions on a triangular lattice, revealing detailed phase competition.

Findings

Identification of Pomeranchuk instability at Van Hove filling with attractive interactions.

Emergence of f-wave and p-wave pairing as filling decreases.

Observation of charge density wave and extended p-wave pairing with repulsive interactions.

Abstract

We study competing orders of spinless fermions in the triangular-lattice Hubbard model with nearest-neighbor interaction. We calculate the effective, momentum-resolved two-particle vertex in an unbiased way in terms of the functional renormalization group method and compare two different schemes for the momentum discretization, one based on dividing the Fermi surface into patches and one based on a channel decomposition. We study attractive and repulsive nearest-neighbor interaction and find a competition of pairing and charge instabilities. In the attractive case, a Pomeranchuk instability occurs at Van Hove filling and $f$-wave and $p$-wave pairing emerge when the filling is reduced. In the repulsive case, we obtain a charge density wave at Van Hove filling and extended $p$-wave pairing with reduced filling. The $p$-wave pairing solution is doubly degenerate and can realize chiral $p+ip$ superconductivity with different Chern numbers in the ground state. We discuss implications for strongly correlated spin-orbit coupled hexagonal electron systems such as moir\'e heterostructures.