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

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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Cited by in corpus (14)

• Realization of Qi-Wu-Zhang model in spin-orbit-coupled ultracold fermions
• The Gross-Neveu-Yukawa Archipelago
• Quantum Simulation of Chiral Phase Transitions
• Quantum Simulation of the N flavor Gross-Neveu Model
• Fermion production at the boundary of an expanding universe: a cold-atom gravitational analogue
• Topological spin-orbit-coupled fermions beyond rotating wave approximation
• Topological and magnetic properties of the interacting Bernevig-Hughes-Zhang model
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• Interacting Dirac fields in an expanding universe: dynamical condensates and particle production
• Chiral spin liquid phase in an optical lattice at mean-field level
• Chiral fermions on lattice axion strings
• Dynamical detection of mean-field topological phases in an interacting Chern insulator
• Topological crystals and soliton lattices in a Gross-Neveu model with Hilbert-space fragmentation
• Emergent Kitaev materials in synthetic Fermi-Hubbard bilayers