Study of Hubbard model on triangular lattices using linearly scaling semi-classical methods*

While several computational techniques, such as 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. Semiclassical methods have been extensively employed to study such systems and have proven to be qualitatively and often quantitatively accurate, especially for weakly correlated materials. Previous studies have demonstrated the effectiveness of combining semi-classical methods and Monte Carlo methods in the Hubbard model on square and cubic lattices, accurately predicting the Neel temperature and aligning with results from Determinant Quantum Monte Carlo (DQMC) calculations.

 

This study aims to assess the efficiency and accuracy of semi-classical methods in frustrated systems, specifically the Hubbard model on a triangular lattice. 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 scales linearly with the system size. This scalability enables us to explore large system sizes, providing valuable insights into the behavior of frustrated systems.