Large-$N$ Chern insulators: lattice field theory and quantum simulation approaches to correlation effects in the quantum anomalous Hall effect

Understand

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.