Interacting fermions on the honeycomb bilayer: from weak to strong coupling

TL;DR

This paper investigates many-body instabilities in half-filled honeycomb bilayer systems across weak to strong coupling regimes, revealing dominant gapped insulating phases with broken symmetries and potential quantum Hall effects, using renormalization group and strong coupling analyses.

Contribution

It provides a comprehensive analysis of interaction-driven phases in honeycomb bilayers, including weak and strong coupling regimes, and extends to spin-1/2 systems with detailed RG equations and ground state constructions.

Findings

Dominant instability often leads to a gapped insulator with broken inversion or time-reversal symmetry.

Weak coupling RG trajectories typically show runaway flows indicating ordering tendencies.

In strong coupling, a phase with inversion symmetry breaking and layer particle imbalance is found.

Abstract

Many-body instabilities of the half-filled honeycomb bilayer are studied using weak coupling renormalization group as well as strong coupling expansion. For spinless fermions and assuming parabolic degeneracy, there are 4-independent four-fermion contact couplings. While the dominant instability depends on the microscopic values of the couplings, the broken symmetry state is typically a gapped insulator with either broken inversion symmetry or broken time reversal symmetry, with a quantized anomalous Hall effect. Under certain conditions, the dominant instability may appear in the particle-particle (pairing) channel. For some non-generic fine-tuned initial conditions, weak coupling RG trajectories flow into the non-interacting fixed point, although generally we find runaway flows which we associate with ordering tendencies. Additionally, a tight binding model with nearest neighbor hopping and nearest neighbor repulsion is studied in weak and strong couplings and in each regime a gapped phase with inversion symmetry breaking is found. In the strong coupling limit, the ground state wavefunction is constructed for vanishing in-plane hopping but finite inter-plane hopping, which explicitly displays the broken inversion symmetry and a finite difference between the number of particles on the two layers. Finally, we discuss the spin-1/2 case and use Fierz identities to show that the number of independent 4-fermion contact couplings is 9. The corresponding RG equations in the spin-1/2 case are also presented, and used to show that, just as in strong coupling, the most dominant weak coupling instability of the repulsive Hubbard model (at half-filling) is an anti-ferromagnet.