Exact Analytical Vortex Solution for a Two-Dimensional Quantum Gas with LHY Correction

In this investigation, we provide an exact analytical vortex solution for a Bose liquid in two dimensions with beyond mean-field correction (BMF). Analytical solutions in two-dimensional systems with BMF corrections are rarely found in the literature. The present result provides a clear framework for understanding vortex structures in low-dimensional quantum fluids and serves as a reliable benchmark for future theoretical and experimental studies.