Hamiltonian Lattice Formulation of Compact Maxwell-Chern-Simons Theory

TL;DR

This paper develops a Hamiltonian lattice formulation for 2+1D compact Maxwell-Chern-Simons theory, analytically solves it, and confirms that the continuum limit reproduces known physical properties, enabling future quantum simulations.

Contribution

It introduces a Hamiltonian lattice framework for the theory, preserving topological features and providing a basis for quantum computational approaches.

Findings

Mass gap matches continuum formula

Topological features are preserved in the lattice formulation

Framework enables future quantum simulations

Abstract

In this paper, a Hamiltonian lattice formulation for 2+1D compact Maxwell-Chern-Simons theory is derived. We analytically solve this theory and demonstrate that the mass gap in the continuum limit matches the well-known continuum formula. Our formulation preserves topological features such as the quantization of the Chern-Simons level, the degeneracy of energy eigenstates, the non-trivial properties of Wilson loops, and the mutual and self statistics of anyons. This work lays the groundwork for future Hamiltonian-based simulations of Maxwell-Chern-Simons theory on classical and quantum computers.