Interaction effect in two-dimensional Dirac fermions

TL;DR

This paper investigates how interactions affect two-dimensional Dirac fermions, revealing the robustness of topological phases in gapped cases and the emergence of charge-density-wave and stripe phases in gapless cases, with implications for correlation-driven topological phases.

Contribution

It provides a detailed numerical analysis of interaction effects on 2D Dirac fermions, showing the stability of topological phases and the emergence of new phases when additional interactions are included.

Findings

Topological phase remains stable in gapped Dirac systems under interactions.

Charge-density-wave and stripe phases appear in gapless Dirac systems.

Additional interactions can suppress the topological phase predicted by mean-field theory.

Abstract

Based on the Dirac equations in the two-dimensional $\pi-$ flux model, we study the interaction effects both in nontrivial gapped and gapless Dirac equations with numerical exact diagonalization method. In the presence of the nearest and next nearest neighbor interactions: for nontrivial gapped Dirac equation, the topological phase is robust and persists in a finite region of the phase diagram; while for gapless Dirac equation, charge-density-wave and stripe phases are identified and the phase diagram in $(V_1, V_2)$ plane is obtained. When the next-next-nearest neighbor interaction is further included to gapless Dirac equation, the topological phase expected in the mean-field theory is absent. Our results are related to the possibility of dynamically generating topological phase from the electronic correlations.