The interplay between strong interactions and the unique environment created by Moire superlattices is believed to be a key for many of the most exciting phenomena seen in these two-dimensional materials. It is then important to treat both one- and two-body effects in a balanced and accurate way. This presents outstanding theoretical, algorithmic, and computational challenges. I will describe our preliminary work on developing and applying quantum Monte Carlo methods to treat Moire systems. This includes a study of the interacting Bistritzer-MacDonald model beyond specialized fillings which are sign-problem-free; calculations in a continuum model of two-dimensional electron gas in Moire potentials; the development of neural quantum state approaches to make more robust detection and prediction of different phases; and the parametrization of an exchange-correlation functional for density-functional theory calculations in two-dimensional materials.

Please contact phweb@ust.hk should you have questions about the talk.