Spectral-Gap Corrections in Finite Open SU(2) Plaquette Strips: Second- and Fourth-Order Results for Two to Five Plaquettes

Abstract

This preprint investigates perturbative spectral-gap corrections in finite open SU(2) plaquette-strip Hamiltonians. An analytical second-order effective Hamiltonian is developed for finite strips, yielding an explicit positive second-order correction to the gap. Fourth-order corrections are computed numerically for systems containing two through five plaquettes, revealing a change in the sign of the fourth-order coefficient between the two- and three-plaquette cases. The calculations are supported by matrix-element checks, direct spectral comparisons, and computational consistency tests. Reproducible Python programs and numerical data accompany the manuscript. The results characterize finite-dimensional models and do not establish a uniform spectral gap in the infinite-volume limit or resolve the four-dimensional Yang–Mills mass-gap problem. The work is presented as a computational and analytical contribution to the study of spectral stability in finite SU(2) lattice systems.