We present a detailed study of the topological Schwinger model [Phys. Rev. D 99, 014503 (2019)], which describes ($1+1$) quantum electrodynamics of an Abelian $U\left(1\right)$ gauge field coupled to a symmetry-protected topological matter sector, by means of a class of ${\mathbb{Z}}_N$ lattice gauge theories. Employing density-matrix renormalization group techniques that exactly implement Gauss' law, we show that these models host a correlated topological phase for different values of $N$, where fermion correlations arise through interparticle interactions mediated by the gauge field. Moreover, by a careful finite-size scaling, we show that this phase is stable in the large-$N$ limit and that the phase boundaries are in accordance with bosonization predictions of the $U\left(1\right)$ topological Schwinger model. Our results demonstrate that ${\mathbb{Z}}_N$ finite-dimensional gauge groups offer a practical route for an efficient classical simulation of equilibrium properties of electromagnetism with topological fermions. Additionally, we describe a scheme for the quantum simulation of a topological Schwinger model exploiting spin-changing collisions in boson-fermion mixtures of ultracold atoms in optical lattices. Although technically challenging, this quantum simulation would provide an alternative to classical density-matrix renormalization group techniques, providing also an efficient route to explore real-time nonequilibrium phenomena.

• Received 30 June 2019

DOI:https://doi.org/10.1103/PhysRevB.100.115152