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

• URL: http://arxiv.org/abs/2111.04485v1
• Date: Mon, 8 Nov 2021 13:22:14 GMT
• Title: Large-$N$ Chern insulators: lattice field theory and quantum simulation approaches to correlation effects in the quantum anomalous Hall effect
• Authors: L. Ziegler, E. Tirrito, M. Lewenstein, S. Hands, and A. Bermudez
• Abstract summary: We give a detailed description of our multidisciplinary approach to understand the fate of the quantum anomalous Hall (QAH) phases. 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 characterise the strongly-coupled fixed points and, moreover, could also explore real-time dynamics and finite-fermion densities.

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