Fluctuation-induced Topological Quantum Phase Transitions in Quantum Spin Hall and Quantum Anomalous Hall Insulators

Abstract

We investigate the role of quantum fluctuations in topological quantum phase transitions of quantum spin Hall insulators and quantum anomalous Hall insulators. Employing the variational cluster approximation to obtain the single-particle Green's function of the interacting many-body system, we characterize different phases by direct calculation of the recently proposed topological order parameter for interacting systems. We pinpoint the influence of quantum fluctuations on the quantum spin Hall to Mott insulator transition in several models. Furthermore, we propose a general mechanism by which a topological quantum phase transition can be driven by the divergence of the self energy induced by interactions.

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• Strong Correlation Effects on Topological Quantum Phase Transitions in Three Dimensions
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• Interplay of local order and topology in the extended Haldane-Hubbard model
• Quantum cluster approach to the spinful Haldane-Hubbard model
• Statistical Analysis of the Chern Number in the Interacting Haldane-Hubbard Model
• Topological Invariant and Quantum Spin Models from Magnetic π Fluxes in Correlated Topological Insulators
• Correlated Topological Phases and Exotic Magnetism with Ultracold Fermions
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• Coexistence of metallic edge states and anti-ferromagnetic ordering in correlated topological insulators
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• Topological Invariants and Ground-State Wave Functions of Topological Insulators on a Torus
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• Characterization of a correlated topological Kondo insulator in one dimension
• Temperature-driven gapless topological insulator
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• Interacting weak topological insulators and their transition to Dirac semimetal phases
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• On Green's function embedding using sum-over-pole representations
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• Topological Gap Opening without Symmetry Breaking from Dynamical Quantum Correlations
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• Short-ranged interaction effects on $Z_2$ topological phase transitions
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• Broken symmetry solutions in one-dimensional lattice models via many-body perturbation theory
• Thermodynamic and topological phase diagrams of correlated topological insulators
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• Short-ranged interaction effects on $Z_2$ topological phase transitions: The perturbative mean-field method
• Comparing the effective enhancement of local and non-local spin-orbit couplings on honeycomb lattices due to strong electronic correlations
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