GPU-accelerated linearly scaling semi-classical methods to study Hubbard model on frustrated lattices

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. Semiclassical methods are a qualitatively and even quantitatively accurate alternative, especially for weakly correlated materials and certain classes of quantum magnets. In this talk, we demonstrate a GPU-accelerated fast solver that scales linearly with system size to study antiferromagnetic T-U phase diagrams in the Hubbard model on 2D and 3D lattices. Furthermore, we assess the efficiency and accuracy of semi-classical methods in applications to the Hubbard model on a triangular lattice and at low temperatures, a difficult problem for conventional quantum Monte Carlo. We utilize the Kernel Polynomial Method for efficient Langevin equation-based sampling of the auxiliary fields introduced during the Hubbard-Stratonovich transformation of the interaction terms. This approach allows us to bypass the computationally expensive matrix diagonalization and slow Monte-Carlo sweep updates, resulting in a computational cost that scales linearly with the system size without losing accuracy. This scalable GPU-accelerated method enables us to explore large system sizes, providing valuable insights into the behavior of correlated and frustrated systems that were not accessible before.