The fundamental nature of the two-dimensional (2D) metal-insulator transition (MIT) and its interplay with magnetic fluctuations remains a highly debated problem in condensed matter physics. Strong electron-electron interactions are posited to be crucial for stabilizing the 2D metallic phase against Anderson localization driven by inherent structural disorder. Building upon our recent investigations—which elucidated the spin-glass nature of the insulating phase in a 1D model with long-range random hopping [1] and utilized large-scale Hartree-Fock simulations to characterize 2D electron glasses in δ-doped layers [2,3]—this project proposes a rigorous, two-pronged extension of our computational framework. First, we will evaluate more generalized models at significantly larger system sizes; this finite-size scaling is critical for definitively distinguishing a sharp phase transition from a crossover regime. Second, we will transcend the static mean-field limitations of the Hartree-Fock approximation by explicitly incorporating thermal and quantum fluctuations utilizing semi-classical and quantum Monte Carlo (QMC) methods.
[1] Xinghai Zhang, and Matthew Foster, Phys. Rev. B 110, 155137 (2024)
[2] Xinghai Zhang, Matthew Foster, and Markus Müller, in preparation
[3] N. D’Anna et al. arXiv:2508.02793