Critical coupling with zero-mode corrections in discretized light-cone quantized $φ^4$ theory

We present an advancement for solving the Discretized Light-Cone Quantization (DLCQ) Hamiltonian for mass spectra in 2D $\phi^4$ theory that incorporates perturbative zero-mode contributions. We demonstrate that this correction accelerates numerical convergence of the mass eigenstates with increasing resolution and yields a critical coupling of comparable accuracy with a substantial reduction in computational costs. Specifically, with more than one order of magnitude reduction in basis space dimensionality we achieve an extrapolated critical coupling of $23.10 \pm 0.25$ compared with $23.53 \pm 0.26$ in the larger basis but without zero-mode correction. We employ Gaussian Process Regression for extrapolation to the continuum limit. The approach we present here is prospective for studies of higher-dimensional gauge theories.