Quantum simulation of the Hubbard model in a moiré superlattice

The Hubbard model, first formulated by physicist John Hubbard in the 1960s, is a simple theoretical model of interacting quantum particles in a lattice. The model is thought to capture the essential physics of high-temperature superconductors, magnetic insulators, and other complex emergent quantum many-body ground states. Although the Hubbard model is greatly simplified as a representation of most real materials, it has nevertheless proved difficult to solve accurately except in the one-dimensional case. Physical realizations of the Hubbard model in two or three dimensions, which can act as quantum simulators, therefore have a vital role to play in solving the strong-correlation puzzle. In this talk, I will discuss a recent experimental realization of the two-dimensional triangular lattice Hubbard model in angle-aligned WSe₂/WS₂ bilayers, which form moiré superlattices because of the difference in lattice constant between the two 2D materials. We obtain a quantum phase diagram of the two-dimensional triangular lattice Hubbard model near the half filling by probing both the charge and magnetic order of the system. Implications for future studies will also be discussed.