Quantum Monte Carlo study of the metal-to-insulator transition on a honeycomb lattice with 1/r interactions

Describing correlated electron systems near phase transitions has been a major challenge in computational condensed-matter physics. In this paper, we apply highly accurate fixed-node quantum Monte Carlo techniques, which directly work with many-body wave functions and simulate electron correlations, to investigate the metal-to-insulator transition of a correlated hydrogen lattice. By calculating spin and charge properties, and analyzing the low-energy Hilbert space, we identify the transition point and identify order parameters that can be used to detect the transition. Our results provide a benchmark for density functional theories seeking to treat correlated electron systems.