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

TL;DR

This paper demonstrates how a modified Haldane model of spinless fermions can realize the Abelian Chern-Simons-Maxwell theory through emergent phenomena, with potential experimental realization in cold atom systems.

Contribution

It shows how the Thirring model and Chern-Simons theory can emerge from a tailored tight-binding model of spinless fermions, bridging condensed matter and topological quantum field theories.

Findings

Realization of the Thirring model in a lattice system.

Identification of confining QED and topological phases.

Feasibility of experimental implementation with cold atoms.

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.