# Electronic Ground State in Bilayer Graphene with Realistic Coulomb Interactions

## TL;DR

This study uses quantum Monte Carlo simulations with realistic Coulomb interactions to determine the ground state of bilayer graphene, confirming the necessity of a finite onsite interaction for insulating behavior and analyzing the influence of interlayer coupling.

## Contribution

It provides non-perturbative evidence that a finite onsite interaction induces an insulating ground state in bilayer graphene with realistic Coulomb interactions.

## Key findings

- A finite critical onsite interaction is required to open a gap in bilayer graphene.
- The critical onsite interaction decreases as interlayer coupling increases.
- Results align with renormalization-group predictions for Hubbard models.

## Abstract

Both insulating and conducting electronic behaviors have been experimentally seen in clean bilayer graphene samples at low temperature, and there is still no consensus on the nature of the interacting ground state at half-filling and in the absence of a magnetic field. Theoretically, several possibilities for the insulating ground states have been predicted for weak interaction strength. However, a recent renormalization-group calculation on a Hubbard model for charge-neutral bilayer graphene with short-range interactions suggests the emergence of low-energy Dirac fermions that would stabilize the metallic phase for weak interactions. Using a non-perturbative projective quantum Monte Carlo, we calculate the ground state for bilayer graphene using a realistic model for the Coulomb interaction that includes both short-range and long-range contributions. We find that a finite critical onsite interaction is needed to gap bilayer graphene, thereby confirming the Hubbard model expectations even in the presence of a long-range Coulomb potential, in agreement with our theoretical renormalization group analysis. In addition, we also find that the critical onsite interactions necessary to destabilize the metallic ground state decreases with increasing interlayer coupling.