**Authors**
: Alessandro Giuliani, Ian Jauslin

**Title:** *
The ground state construction of bilayer graphene
*

**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.
*

Alessandro Giuliani

Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre,

L.go S.L. Murialdo, 1, 00146 Roma, Italy.

Ian Jauslin

University of Rome "Sapienza", Dipartimento di Fisica,

P.le Aldo Moro, 2, 00185 Roma, Italy