Diagnostics For The Laughlin Wavefunction Through The Metropolis Hastings Algorithm

Fractional Quantum Hall Effect (FQHE) suggests the existence of a new state of matter with fractional excitations and statistics. Laughlin proposed an Ansatz that could approximate and theoretically explain a system that pertains to FQHE but this is a quantum many-body problem that has no analytical solution up until now. Studies on 2D materials such as bilayer graphene and twisted molybdenum ditelluride (tMoTe2) have shown that these materials are good for advancing the knowledge about this quantum many-body problem.

We simulate a 2D electron gas (2DEG) using Metropolis Hastings Monte Carlo to gain insights into this problem. Using the proposed Laughlin Wavefunction, we learn that the new state of matter is a liquid at high fictitious temperature and a crystal at low fictitious temperature. This talk will focus on the numerical method employed for the quantum many-body problem and suggest where the transition from liquid phase to crystal phase happens.