Ian Jauslin

## The ground state contruction of bilayer graphene

2015

### 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 that the pressure and two point Schwinger function, away from its singularities, are analytic 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.

PDF:

LaTeX source:
• tarball: 15gij-1.0.1.tar.gz
• git repository: 15gij-git (the git repository contains detailed information about the changes in the paper as well as the source code for all previous versions).

### Talks

This work has been presented at the following conferences:

• [Pri17]: Ground state construction of bilayer graphene
Princeton University, New Jersey, USA, Mar 30 2017
pdf, source

• [QMa16]: Ground state construction of bilayer graphene
Qmath13, GeorgiaTech, Atlanta, Georgia, USA, Oct 09 2016
pdf, source

• [Obe16]: Ground state construction of bilayer graphene
Oberwolfach Workshop 1637, Germany, Sep 12 2016
pdf, source

• [PhD16]: The renormalization group in the weak- and strong-coupling regimes
PhD defense, University of Rome "Sapienza", Rome, Italy, Jan 22 2016
pdf, source

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