Infinite product expansion and Monte Carlo methods for frustrated magnetism

The conventional Monte Carlo methods applied to the Kondo lattice model and the Kitaev model rely on classical techniques involving exact diagonalization of the Hamiltonian. However, these methods do not exploit the sparsity of the Hamiltonian matrix, leading to prohibitively high computational costs. To overcome this limitation, we have developed a novel infinite product expansion (iPE) method, which we have successfully integrated into Monte Carlo simulations for both models. This new approach significantly reduces the computational complexity from O(N^3)/O(N^4) to O(N)/O(N^2), where N represents the system size. Consequently, simulations of the Kitaev and Kondo lattice models have become dramatically faster, with improved scalability. This advancement paves the way for exploring new topological phase transitions in the three-dimensional Kitaev model and discovering novel topological excitations in frustrated Kondo lattice models by enabling research on larger system sizes. We also plan to present unbiased simulations of future quantum systems for both cases.