Quantum Anomalous Hall Insulator Stabilized By Competing Interactions

TL;DR

This paper investigates how interactions in a spinless fermion system on a checkerboard lattice induce various quantum phases, notably revealing a quantum anomalous Hall phase driven by competing interactions, supported by multiple analytical and numerical methods.

Contribution

It demonstrates that both repulsive and attractive interactions can induce a quantum anomalous Hall phase in a quadratic band touching semimetal, clarifying the phase diagram and ruling out the nematic semimetal at weak coupling.

Findings

Identification of a quantum anomalous Hall phase driven by interactions.

Determination of phase boundaries in the interaction parameter space.

Absence of the nematic semimetal at weak coupling.

Abstract

We study the quantum phases driven by interaction in a semimetal with a quadratic band touching at the Fermi level. By combining the density matrix renormalization group (DMRG), analytical power expanded Gibbs potential method, and the weak coupling renormalization group, we study a spinless fermion system on a checkerboard lattice at half-filling, which has a quadratic band touching in the absence of interaction. In the presence of strong nearest-neighbor ($V_1$) and next-nearest-neighbor ($V_2$) interactions, we identify a site nematic insulator phase, a stripe insulator phase, and a phase separation region, in agreement with the phase diagram obtained analytically in the strong coupling limit (i.e. in the absence of fermion hopping). In the intermediate interaction regime, we establish a quantum anomalous Hall phase in the DMRG as evidenced by the spontaneous time-reversal symmetry breaking and the appearance of a quantized Chern number $C = 1$. For weak interaction, we utilize the power expanded Gibbs potential method that treats $V_1$ and $V_2$ on equal footing, as well as the weak coupling renormalization group. Our analytical results reveal that not only the repulsive $V_1$ interaction, but also the $V_2$ interaction (both repulsive and attractive), can drive the quantum anomalous Hall phase. We also determine the phase boundary in the $V_1$-$V_2$ plane that separates the semimetal from the quantum anomalous Hall state. Finally, we show that the nematic semimetal, which was proposed for $|V_2| \gg V_1$ at weak coupling in a previous study, is absent, and the quantum anomalous Hall state is the only weak coupling instability of the spinless quadratic band touching semimetal.