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Hamiltonian lattice formulation of compact Maxwell-Chern-Simons theory

Changnan Peng1, Maria Cristina Diamantini2, Lena Funcke3, Syed Muhammad Ali Hassan4, Karl Jansen4,5, Stefan Kühn5, Di Luo1,6,7, and Pranay Naredi4,5

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Phys. Rev. D 114, 034511 – Published 13 August, 2026

DOI: https://doi.org/10.1103/rrzw-s456

Abstract

In this paper, we derive a Hamiltonian lattice formulation of the 2+1D 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.

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Phys. Rev. D 114, 034511– Published 13 August, 2026
  • Received 18 October 2025
  • Accepted 7 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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