Coulomb correlations in the honeycomb lattice: role of translation symmetry

TL;DR

This study compares two cluster methods for analyzing Coulomb correlations in the honeycomb lattice, showing that translation symmetry preservation in DCA leads to different predictions of semi-metallic versus insulating phases.

Contribution

It demonstrates that the dynamical cluster approximation (DCA) preserves translation symmetry unlike CDMFT, significantly affecting the predicted electronic phases in the Hubbard model.

Findings

DCA predicts semi-metallic behavior at small U due to translation symmetry.

CDMFT shows a spurious gap at small U because it violates translation symmetry.

At large U, both methods agree on Mott insulating behavior.

Abstract

The effect of Coulomb correlations in the half-filled Hubbard model of the honeycomb lattice is studied within the dynamical cluster approximation (DCA) combined with exact diagonalization (ED) and continuous-time quantum Monte Carlo (QMC). The important difference between this approach and the previously employed cluster dynamical mean field theory (CDMFT) is that DCA preserves the translation symmetry of the system, while CDMFT violates this symmetry. As the Dirac cones of the honeycomb lattice are the consequence of perfect long-range order, DCA yields semi-metallic behavior at small onsite Coulomb interactions $U$, whereas CDMFT gives rise to a spurious excitation gap even for very small $U$. This basic difference between the two cluster approaches is found regardless of whether ED or QMC is used as the impurity solver. At larger values of $U$, the lack of translation symmetry becomes less important, so that the CDMFT reveals a Mott gap, in qualitative agreement with large-scale QMC calculations. In contrast, the semi-metallic phase obtained in DCA persists even at $U$ values where CDMFT and large-scale QMC consistently show Mott insulating behavior.