# Numerical evidence of conformal phase transition in graphene with long-range interactions

## TL;DR

This study uses advanced simulations to investigate phase transitions in graphene, finding that a scaled-up interaction strength induces a semimetal to spin-density wave transition, with evidence suggesting a conformal phase transition rather than a traditional universality class.

## Contribution

The paper provides the first unbiased simulation evidence of a conformal phase transition in graphene with long-range interactions and introduces an improved HMC algorithm for such studies.

## Key findings

- A 1.6x increase in interaction strength induces a SDW transition in graphene.
- No evidence found for charge-density wave order.
- Results favor a conformal phase transition over the predicted universality class.

## Abstract

Using state of the art Hybrid-Monte-Carlo (HMC) simulations we carry out an unbiased study of the competition between spin-density wave (SDW) and charge-density wave (CDW) order in suspended graphene. We determine that the realistic inter-electron potential of graphene must be scaled up by a factor of roughly 1.6 to induce a semimetal-SDW phase transition and find no evidence for CDW order. A study of critical properties suggests that the universality class of the three-dimensional chiral Heisenberg Gross-Neveu model with two fermion flavors, predicted by renormalization group studies and strong-coupling expansion, is unlikely to apply to this transition. We propose that our results instead favor an interpretation in terms of a conformal phase transition. In addition, we describe a variant of the HMC algorithm which uses exact fermionic forces during molecular dynamics trajectories and avoids the use of pseudofermions. Compared to standard HMC this allows for a substantial increase of the integrator stepsize while achieving comparable Metropolis acceptance rates and leads to a sizable performance improvement.