Quantum Monte Carlo study of artificial triangular graphene quantum dots

We investigate the magnetic phases of semiconductor-based artificial triangular graphene quantum dots (TGQDs) with zigzag edges using variational and diffusion Monte Carlo methods. These systems serve as quantum simulators for bipartite lattices with broken sublattice symmetry, providing a platform to study the extended Hubbard model's emergent magnetic phenomena, including Lieb's magnetism at half filling, edge depolarization upon single-electron addition, and Nagaoka ferromagnetism. Our nonperturbative quantum Monte Carlo simulations, performed for finite-sized TGQDs modeled as nanopatterned GaAs quantum wells, with system sizes up to Ns = 61 lattice sites, reveal a transition from metallic to insulating regimes as a function of the quantum well radius rho, while preserving edge-polarized ground states at half filling. Notably, edge depolarization occurs upon single-electron doping in both metallic and insulating phases, in contrast to the Nagaoka ferromagnetism observed in hexagonal armchair geometries.