Diagnosis of interaction-driven topological phase via exact diagonalization

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.

5 pages, 3 figures, 1 table in the main text; 4 pages, 7 figures, 1 table in the supplemental material

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Cited by in corpus (31)

• Interacting topological insulators: a review
• Symmetry-Breaking Topological Insulators in the ${\mathbb{Z}}_2$ Bose-Hubbard Model
• Diagnosis of interaction-driven topological phase via exact diagonalization
• Dynamical Generation of Topological Masses in Dirac Fermions
• Interplay of local order and topology in the extended Haldane-Hubbard model
• Tunning topological phase and quantum anomalous Hall effect by interaction in quadratic band touching systems
• The fate of interaction-driven topological insulators under disorder
• Large Band Gap Quantum Anomalous Hall Phase in Hexagonal Organometallic Frameworks
• Quantum Anomalous Hall Insulator Stabilized By Competing Interactions
• Emergence of topological Mott insulators in proximity of quadratic band touching points
• Interplay of interactions, disorder and topology in the Haldane-Hubbard model
• Thermodynamic Response and Neutral Excitations in Integer and Fractional Quantum Anomalous Hall States Emerging from Correlated Flat Bands
• Stability of two-dimensional asymmetric materials with a quadratic band crossing point under four-fermion interaction and impurity scattering
• Topological phase transitions with SO(4) symmetry in (2+1)d interacting Dirac fermions
• Self-Trapped Polarons and Topological Defects in a Topological Mott Insulator
• Quantum Anomalous Hall Phase Stabilized via Realistic Interactions on a Kagome Lattice
• Quantum anomalous Hall state from spatially decaying interactions on the decorated honeycomb lattice
• Antiferromagnetic transitions of Dirac fermions in three dimensions
• Interaction-driven Quantum Anomalous Hall Effect in Halogenated Hematite Nanosheets
• Robust measurement of wave function topology on NISQ quantum computers
• Fermion-fermion interaction driven instability and criticality of quadratic band crossing systems with the breaking of time-reversal symmetry
• Interaction-driven quantum anomalous Hall insulator in Dirac semimetal
• Bosonic Topological Excitations from the Instability of a Quadratic Band Crossing
• Phase transitions in the Haldane-Hubbard model with ionic potentials
• Anatomy of plasmons in generic Luttinger semimetals
• Higher-order topological insulator in a modified Haldane-Hubbard model
• Chirality-2 fermion induced anti-Klein tunneling in 2D checkerboard lattice
• Topological phases in pseudospin-1 Fermi gases with two-dimensional spin-orbit coupling
• Interaction Driven Topological Phase Transition in Monolayer CrCl${}_2$(pyrazine)${}_2$
• Ubiquitous nematic Dirac semimetal emerging from interacting quadratic band touching system
• Quantum anomalous Hall domains in a Quenched Topological Mott Insulator