Hamiltonian lattice formulation of compact Maxwell-Chern-Simons theory

In this paper, we derive a Hamiltonian lattice formulation of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mn>2</a:mn> <a:mo>+</a:mo> <a:mn>1</a:mn> <a:mi mathvariant="normal">D</a:mi> </a:mrow> </a:math> compact Maxwell-Chern-Simons theory within the zero instanton sector. We analytically solve the model and show that the mass gap in the continuum limit precisely reproduces the well-known continuum result. The formulation preserves key topological features, including the quantization of the Chern-Simons level, the degeneracy of energy eigenstates, the nontrivial properties of Wilson loops, and the mutual and self-statistics of anyons. By reconciling gauge compactness, locality, and canonical quantization within a unified framework, this work provides a foundation for conceivable future Hamiltonian-based simulations of lattice Maxwell-Chern-Simons theory. It aims to bridge topological field theory and quantum information science, with the goal of enabling Hamiltonian-based quantum simulations of Maxwell-Chern-Simons theory on both classical and quantum computers.