The ground state construction of bilayer graphene

TL;DR

This paper rigorously constructs the ground state of half-filled bilayer graphene with interactions, revealing a degenerate Fermi surface with symmetry-protected points and interaction-renormalized locations, using fermionic renormalization group methods.

Contribution

It provides a rigorous ground state construction for bilayer graphene considering dominant hopping parameters and short-range interactions, with a detailed analysis of Fermi surface and energy regimes.

Findings

Degenerate Fermi surface with eight points, two symmetry-protected.

Interaction-renormalized Fermi point locations.

Conical dispersion relation at Fermi points.

Abstract

We consider a model of half-filled bilayer graphene, in which the three dominant Slonczewski-Weiss-McClure hopping parameters are retained, in the presence of short range interactions. Under a smallness assumption on the interaction strength $U$ as well as on the inter-layer hopping $\epsilon$, we construct the ground state in the thermodynamic limit, and prove its analyticity in $U$, uniformly in $\epsilon$. The interacting Fermi surface is degenerate, and consists of eight Fermi points, two of which are protected by symmetries, while the locations of the other six are renormalized by the interaction, and the effective dispersion relation at the Fermi points is conical. The construction reveals the presence of different energy regimes, where the effective behavior of correlation functions changes qualitatively. The analysis of the crossover between regimes plays an important role in the proof of analyticity and in the uniform control of the radius of convergence. The proof is based on a rigorous implementation of fermionic renormalization group methods, including determinant estimates for the renormalized expansion.