Speaker
Description
The Hubbard model offers a powerful minimal description of molecules and materials, yet it neglects several effects and interactions observed in nature that give rise to a much richer variety of physics. For instance, extending the on-site interaction to include nonlocal interactions gives rise to a competition between strongly correlated phases, while incorporating spin-orbit coupling can lead to the emergence of exotic topological phases. With this in mind, we aim to develop a more realistic platform for simulating graphene and, potentially, other materials with similar lattice structures, such as transition metal dichalcogenides (TMDs). Specifically, we consider the extended Kane-Mele-Hubbard model, which features a Kane-Mele spin-orbit coupling term and nearest neighbor electron-electron interactions.
Simulating this model is particularly challenging when the nonlocal interactions become dominant over the on-site Hubbard interaction, where one encounters a severe sign problem at half-filling. For this reason, this regime has largely been avoided in the literature, and the Kane-Mele term likely compounds this difficulty further by introducing a complex phase at the level of the connectivity matrix. To investigate this regime, we develop a continuous auxiliary field formulation of the extended Kane-Mele-Hubbard model suitable for treatment with the Hybrid Monte Carlo (HMC) algorithm. Using this formalism, we characterize the severity of the sign problem across the model's parameter space, with the aim of establishing feasible regions of simulations, as a first step toward mapping out the model's full phase diagram.