Lattice Gauge Theories for Quantum Matter and Quantum Information

Lattice gauge theories describe gauge interactions in high-energy physics and emergent gauge structures in quantum matter. Their non-Abelian realizations are particularly relevant to topological quantum computation and quantum simulation. Our goal is to determine the general structure of the phase diagrams of lattice gauge theories based on discrete non-Abelian groups.

We report recent advances in this direction. Exact diagonalization reveals symmetry-protected degeneracies in the magnetic limit that match the anyon content of the corresponding quantum double models and appear to persist away from this limit, while the electric-limit spectrum is analysed using representation theory. In parallel, we develop a Euclidean Monte Carlo formulation to study larger systems and characterize the phases and transitions of these theories.