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



Ziegler, L, Tirrito, E, Lewenstein, M, Hands, S ORCID: 0000-0001-5720-7852 and Bermudez, A
(2022) Large-N Chern insulators: Lattice field theory and quantum simulation approaches to correlation effects in the quantum anomalous Hall effect. Annals of Physics, 439. p. 168763.

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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 characterize the strongly-coupled fixed points and, moreover, could also explore real-time dynamics and finite-fermion densities.

Item Type: Article
Uncontrolled Keywords: Correlated Chern insulators, Quantum anomalous Hall effect, Four-Fermi lattice field theories, Large-N methods, tensor networks
Divisions: Faculty of Science and Engineering > School of Physical Sciences
Depositing User: Symplectic Admin
Date Deposited: 02 Mar 2022 09:23
Last Modified: 18 Jan 2023 21:11
DOI: 10.1016/j.aop.2022.168763
Open Access URL: https://www.sciencedirect.com/science/article/pii/...
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URI: https://livrepository.liverpool.ac.uk/id/eprint/3149926