%0 Journal Article
%A Ziegler, L.
%A Tirrito, E.
%A Lewenstein, M.
%A Hands, S.
%A Bermúdez Carballo, Alejandro
%T Large-N Chern insulators: lattice field theory and quantum simulation approaches to correlation effects in the quantum anomalous Hall effect
%D 2022
%@ 0003-4916
%U https://hdl.handle.net/20.500.14352/71560
%X Four-Fermi quantum field theories in (2+1) dimensions lie among the simplest models in high-energy physics, the understanding of which requires a non-perturbative lattice formulation addressing their strongly-coupled fixed points. These lattice models are also relevant in condensed matter, as they offer a neat playground to explore strong correlations in the quantum anomalous Hall (QAH) effect. We give a detailed description of our multidisciplinary approach to understand the fate of the QAH phases as the four-Fermi interactions are increased, which combines strong-coupling and effective-potential techniques, unveiling a rich phase diagram with large -N Chern insulators and Lorentz breaking fermion condensates. Moreover, this toolbox can be enlarged with recent advances in quantum information science, as we show that tensor-network algorithms based on projected entangled pairs can be used to improve our understanding of the strong-coupling limit. We also present a detailed scheme that uses ultra-cold atoms in optical lattices with synthetic spin- orbit coupling to build quantum simulators of these four-Fermi models. This yields a promising alternative to characterize the strongly-coupled fixed points and, moreover, could also explore real-time dynamics and finite-fermion densities.(c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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