# Interactions and phase transitions on graphene's honeycomb lattice.

@article{Herbut2006InteractionsAP, title={Interactions and phase transitions on graphene's honeycomb lattice.}, author={Igor F. Herbut}, journal={Physical review letters}, year={2006}, volume={97 14}, pages={ 146401 } }

The low-energy theory of interacting electrons on graphene's two-dimensional honeycomb lattice is derived and discussed. In particular, the Hubbard model in the large-N limit is shown to have a semimetal-antiferromagnetic insulator quantum critical point in the universality class of the Gross-Neveu model. The same equivalence is conjectured to hold in the physical case N=2, and its consequences for various physical quantities are examined. The effects of the long-range Coulomb interaction and…

## Figures from this paper

## 252 Citations

Charge Order in the Holstein Model on a Honeycomb Lattice.

- PhysicsPhysical review letters
- 2019

It is shown that Dirac fermions give rise to charge-density-wave (CDW) order and present evidence that this occurs only above a finite critical interaction strength, and the temperature for the transition into the CDW which can occur at finite values owing to the discrete nature of the broken symmetry.

Hidden charge order of interacting Dirac fermions on the honeycomb lattice

- PhysicsPhysical Review B
- 2018

We consider the extended half-filled Hubbard model on the honeycomb lattice for second nearest-neighbor interactions. Using a functional integral approach, we find that collective fluctuations…

Spin-Liquid Phase in the Hubbard Model on the Honeycomb Lattice

- PhysicsHigh Performance Computing in Science and Engineering
- 2010

It is concluded that a quantum spin liquid, lacking any conventional order, emerges with local charge and spin correlations, best described by a resonating valence bonds state.

Coulomb interaction and magnetic catalysis in the quantum Hall effect in graphene

- Physics
- 2012

The dynamics of symmetry breaking responsible for lifting the degeneracy of the Landau levels (LLs) in the integer quantum Hall (QH) effect in graphene is studied in a low-energy model with the…

Gap generation and semimetal-insulator phase transition in graphene

- Physics
- 2010

The gap generation is studied in suspended clean graphene in the continuum model for quasiparticles with the Coulomb interaction. We solve the gap equation with the dynamical polarization function…

Dynamics in the quantum Hall effect and the phase diagram of graphene

- Physics
- 2008

The dynamics responsible for lifting the degeneracy of the Landau levels in the quantum Hall (QH) effect in graphene is studied by utilizing a low-energy effective model with a contact interaction. A…

Controllability of ferromagnetism in graphene

- Physics
- 2010

We systematically study magnetic correlations in graphene within Hubbard model on a honeycomb lattice by using quantum Monte Carlo simulations. In the filling region below the Van Hove singularity,…

Pinning the Order: The Nature of Quantum Criticality in the Hubbard Model on Honeycomb Lattice

- Physics
- 2013

A new algorithm of quantum Monte Carlo simulations designed to detect very weak magnetic order allows high-resolution studies of the correlation between magnetic order and electrical insulation in…