Abelian Chern-Simons-Maxwell theory from a tight binding model of spinless fermions

Abstract

Abelian Chern-Simons-Maxwell theory can emerge from the bosonisation of the 2+1-dimensional Thirring model that describes interacting Dirac fermions. Here we show how the Thirring model manifests itself in the low energy limit of a two-dimensional tight-binding model of spinless fermions. To establish that we employ a modification of Haldane's model, where the "doubling" of fermions is rectified by adiabatic elimination. Subsequently, fermionic interactions are introduced that lead to the analytically tractable Thirring model. By local density measurements of the lattice fermions we can establish that for specific values of the couplings the model exhibits the confining 2+1-dimensional QED phase or a topological ordered phase that corresponds to the Chern-Simons theory. The implementation of the model as well as the measurement protocol are accessible with current technology of cold atoms in optical lattices.

4.5 pages, 2 figures, version to appear in PRL

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• Cold atom simulation of interacting relativistic quantum field theories
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• Duality between 3D Massive Thirring and Maxwell Chern-Simons models from 2D bosonization
• Collective modes in a Dirac insulator with short range interactions
• Fractonic self-duality and covariant magnetic fractons
• Effective field theories for interacting boundaries of 3D topological crystalline insulators through bosonisation
• Emergence of charge density wave and superconducting phase transitions through Lorentz-invariant interactions in the Haldane-Hubbard model
• Quantum geometric tensors from sub-bundle geometry
• A Two-Gauge Field Model for Magnetoelectric Boundaries
• Excitonic gap generation in thin-film topological insulators
• Edge states and anomalous SUSY in (2+1)-dimensional Maxwell Chern-Simons theory