Toward Hamiltonian simulations of Maxwell-Chern-Simons theory: constant modes and gauge field truncation

• URL: http://arxiv.org/abs/2607.00082v1
• Date: Tue, 30 Jun 2026 18:01:35 GMT
• Title: Toward Hamiltonian simulations of Maxwell-Chern-Simons theory: constant modes and gauge field truncation
• Abstract summary: Maxwell-Chern-Simons (MCS) theory in $2+1$ dimensions provides a paradigmatic example of a topological gauge theory with both dynamical and topological degrees of freedom.<n>Being analytically solvable in the continuum, it provides an ideal benchmark for understanding how the topological properties of the theory are encoded in a finite-dimensional lattice Hilbert space.
• Score: 1.8641283062016065
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Maxwell-Chern-Simons (MCS) theory in $2+1$ dimensions provides a paradigmatic example of a topological gauge theory with both dynamical and topological degrees of freedom. Its Euclidean formulation suffers from a sign problem, making Hamiltonian numerical approaches particularly attractive. As a first step toward the non-perturbative Hamiltonian study of MCS theory, we investigate the constant mode sector on a spatial torus. Being analytically solvable in the continuum, it provides an ideal benchmark for understanding how the topological properties of the theory are encoded in a finite-dimensional lattice Hilbert space. We construct a finite-dimensional discretization of the torus of flat connections and show that the resulting lattice problem maps onto a generalized Harper-Hofstadter model with twisted boundary conditions. We identify the commensurability conditions under which the finite lattice exactly reproduces the magnetic translation algebra and the topological degeneracy of the continuum theory. A systematic analysis of gauge field truncation and its convergence toward the continuum limit is then presented.

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