Interaction driven phases in the honeycomb lattice from exact diagonalization

TL;DR

This study uses exact diagonalization to explore interaction-driven phases in the honeycomb lattice, confirming some predicted phases and challenging the existence of a mean-field predicted Chern insulator phase.

Contribution

It provides numerical evidence for certain ordered phases and questions the realization of the Haldane phase in finite systems.

Findings

Evidence for charge density wave, Kekulé bond order, and sublattice charge modulation.

No clear sign of the interaction-driven Chern insulator (Haldane) phase.

Characterization of phases via ground state degeneracy and correlation functions.

Abstract

We investigate the fate of interaction driven phases in the half-filled honeycomb lattice for finite systems via exact diagonalization with nearest and next nearest neighbour interactions. We find evidence for a charge density wave phase, a Kekul\'e bond order and a sublattice charge modulated phase in agreement with previously reported mean-field phase diagrams. No clear sign of an interaction driven Chern insulator phase (Haldane phase) is found despite being predicted by the same mean-field analysis. We characterize these phases by their ground state degeneracy and by calculating charge order and bond order correlation functions.