Statistical Analysis of the Chern Number in the Interacting Haldane-Hubbard Model

Abstract

In the context of many-body interacting systems described by a topological Hamiltonian, we investigate the robustness of the Chern number with respect to different sources of error in the self-energy. In particular, we analyze the importance of non-local (momentum dependent) vs. local contributions to the self-energy and show that the local self-energy provides a qualitative description of the topological phase diagrams of many-body interacting systems, whereas the explicit momentum-dependence constitutes a correction to the exact location of the phase transition. For the latter, we propose a statistical analysis, on the basis of which we develop a stochastic upper bound for the uncertainty of the Chern number as a function of the amount of momentum-dependence of the self-energy. We apply this analysis to the Haldane-Hubbard model and discuss the implications of our results for a general class of many-body interacting systems.

arXiv comment9 pages, 7 figures

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• Dynamical Mean-Field Theory of Strongly Correlated Electron Systems
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• Lattice symmetry and emergence of antiferromagnetic quantum Hall states
• Topological Green function of interacting systems
• Improved effective vertices in the multi-orbital Two-Particle Self-Consistent method from Dynamical Mean-Field Theory
• Engineering Topological Phases Guided by Statistical and Machine Learning Methods
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• Topological Anderson insulating phases in the interacting Haldane model
• Phase transitions in the Haldane-Hubbard model with ionic potentials
• Local vs non-local correlation effects in interacting quantum spin Hall insulators
• A semimetallic square-octagon (fes) two-dimensional polymer with high mobility
• Antiferromagnetic Chern insulator with large charge gap in heavy transition-metal compounds
• Topological phase in the extended Haldane-Hubbard model with sublattice-dependent repulsion
• The odd-parity altermagnetism: A spin group study
• Phase diagram of the interacting Haldane model with spin-dependent sublattice potentials
• On valley asymmetry in a topological interaction for quasi-particles
• Incipient quantum spin Hall insulator under strong correlations
• Antiferromagnetic topological insulators in heavy-fermion systems
• Towards a Topological Quantum Chemistry description of correlated systems: the case of the Hubbard diamond chain
• High-Temperature Quantum Anomalous Hall Effect in Buckled Honeycomb Antiferromagnets