(\mathbb{Z}_N\) gauge theories coupled to topological fermions: QED\(_2\) with a quantum-mechanical \(\theta\) angle

• Published in: arXiv.org 2019-09
• Main Authors: Magnifico, G, Vodola, D, Ercolessi, E, Kumar, S P, Müller, M, Bermudez, A
• Format: Article
• Language: English
• Subjects: Cold spinning; Computer simulation; Density; Electromagnetism; Fermions; Optical lattices; Particle interactions; Quantum electrodynamics; Simulation; Topology; Ultracold atoms
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1906.07005

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 \(U(1)\) 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 inter-particle 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 to bosonization predictions of the \(U(1)\) 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 ultra-cold 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 non-equilibrium phenomena.