Lena Funcke, University of Bonn

Chern-Simons theory is a topological quantum field theory with numerous applications in condensed matter and high-energy physics, including the study of anomalies, fermion/boson dualities, and the fractional quantum Hall effect. The lattice formulation of pure Chern-Simons theory faces a doubling problem, which can be resolved by incorporating a Maxwell term, resulting in Maxwell-Chern-Simons theory. While the Lagrangian formulation for Euclidean spacetime lattices has been recently derived, a Hamiltonian formulation remains absent.

In this work, we address this gap by deriving a Hamiltonian lattice formulation of compact Maxwell-Chern-Simons theory using the Villain approximation. We analytically solve this theory and show that the mass gap in the continuum limit matches the well-known continuum formula. The inclusion of fermions necessitates numerical methods, but standard Monte Carlo simulations cannot simulate the theory due to the sign problem. Our Hamiltonian formulation of Maxwell-Chern-Simons theory lays the groundwork for future Hamiltonian-based simulations of the theory on classical and quantum computers.