Diagnosis of interaction-driven topological phase via exact diagonalization

TL;DR

This paper introduces a method using exact diagonalization to identify interaction-driven topological phases by analyzing eigenvalues and correlation functions, demonstrated on spinless fermions on a checkerboard lattice.

Contribution

The paper presents a novel scheme combining eigenvalue analysis and correlation functions to diagnose topological phases in small systems via exact diagonalization.

Findings

Evidence of a quantum anomalous Hall phase driven by weak interactions

Identification of a first-order transition to a nematic Mott insulator

Validation of the scheme on a checkerboard lattice model

Abstract

We propose a general scheme for diagnosing interaction-driven topological phases in the weak interaction regime using exact diagonalization (ED). The scheme comprises the analysis of eigenvalues of the point-group operators for the many-body eigenstates and the correlation functions for physical observables to extract the symmetries of the order parameters and the topological numbers of the underlying ground states at the thermodynamic limit from a relatively small size system afforded by ED. As a concrete example, we investigate the interaction effects on the half-filled spinless fermions on the checkerboard lattice with a quadratic band crossing point. Numerical results support the existence of a spontaneous quantum anomalous Hall phase purely driven by a nearest-neighbor weak repulsive interaction, separated from a nematic Mott insulator phase at strong repulsive interaction by a first-order phase transition.