Study of Hubbard model on frustrated systems using efficient semi-classical methods

While computational techniques like Quantum Monte Carlo (QMC), have achieved remarkable success in investigating strongly correlated lattice models, they often face challenges in obtaining reliable results for systems with itinerant electrons, geometric frustration, or realistic electronic interactions like spin-orbit coupling. For example, QMC methods applied to frustrated systems must contend with the infamous sign problem. Semiclassical methods have recently emerged as a qualitatively and even quantitatively accurate alternative, especially for weakly correlated materials and certain classes of quantum magnets. Previous studies have demonstrated the effectiveness of combining semi-classical methods for the Hubbard model on square and cubic lattices, accurately predicting the Neel temperature and aligning with results from Determinant Quantum Monte Carlo (DQMC) calculations. In this talk, we assess the efficiency and accuracy of semi-classical methods in applications to the Hubbard model on a triangular lattice, a difficult problem for conventional QMC. We utilize the Kernel Polynomial Method (KPM) for efficient Monte Carlo sampling of the auxiliary fields introduced during the Hubbard-Stratonovich transformation of the interaction terms. The KPM approach allows us to bypass the computationally expensive matrix diagonalization, resulting in a computational cost that can scale linearly with the system size without losing accuracy. This scalability enables us to explore large system sizes, providing valuable insights into the behavior of frustrated systems.