Interaction-driven quantum anomalous Hall insulator in Dirac semimetal

TL;DR

This paper demonstrates that in a Dirac semimetal on a checkerboard lattice, strong enough interactions induce a quantum anomalous Hall insulator with quantized Hall conductance, confirmed through numerical simulations.

Contribution

It reveals the emergence of a QAH phase driven by interactions in a Dirac semimetal, using combined analytical and numerical methods.

Findings

QAH phase appears at finite interaction strength

QAH state exhibits spontaneous time-reversal symmetry breaking

Quantized Chern number C=1 confirmed numerically

Abstract

The interaction-driven quantum anomalous Hall (QAH) insulator has been sought for a long time in a Dirac semimetal with linear band touching points at the Fermi level. By combining exact diagonalization, density matrix renormalization group, and analytical methods, we study a spinless fermion system on the checkerboard lattice with two fold rotational symmetry, which realizes two Dirac band touching points in the absence of interaction. At weak coupling, the Dirac semimetal is stable. At a finite density-density repulsive interaction, we analyze possible symmetry broken states, and find that an QAH state is stabilized when the interaction strength exceeds the energy scale controlling the separation between the Dirac points. Through numerical simulations, we verify the existence of the QAH phase with spontaneous time-reversal symmetry breaking and quantized Chern number $C = 1$.