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arXiv · 1905.02218

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

Thomas Mertz·Karim Zantout·Roser Valentí
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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.

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Thomas Mertz, Karim Zantout, Roser Valentí. 2019-06-03. Statistical Analysis of the Chern Number in the Interacting Haldane-Hubbard Model. https://doi.org/10.1103/physrevb.100.125111

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