Study of Hubbard model on triangular lattices using linearlyscaling semi-classical methods

While several computational techniques, such as Quantum MonteCarlo (QMC), have achieved remarkable success in investigatingstrongly correlated lattice models, they often face challenges inobtaining reliable results for systems with itinerant electrons,geometric frustration, or realistic electronic interactions like spin-orbitcoupling. Semiclassical methods have been extensively employed tostudy such systems and have proven to be qualitatively and oftenquantitatively accurate, especially for weakly correlated materials.Previous studies have demonstrated the effectiveness of combiningsemi-classical methods and Monte Carlo methods in the Hubbardmodel on square and cubic lattices, accurately predicting the Neeltemperature and aligning with results from Determinant QuantumMonte Carlo (DQMC) calculations. This study aims to assess the efficiency and accuracy of semi-classical methods in frustrated systems, specifically the Hubbardmodel on a triangular lattice. We utilize the Kernel Polynomial Method(KPM) for efficient Monte Carlo sampling of the auxiliary fieldsintroduced during the Hubbard-Stratonovich transformation of theinteraction terms. The KPM approach allows us to bypass thecomputationally expensive matrix diagonalization, resulting in acomputational cost that scales linearly with the system size. Thisscalability enables us to explore large system sizes, providingvaluable insights into the behavior of frustrated systems.