Seminar
＜10/2024＞- Date
- 10月28日（月）14:00-
- Speaker
- 山田昌彦（東大理）
- Title
- Introduction and development of Monte Carlo methods and the application of the infinite product expansion
The Monte Carlo methods used in the Kondo lattice model and the Kitaev model are both classical Monte Carlo methods that include full exact diagonalization of the Hamiltonian in the calculation process. For this reason, the sparsity of the Hamiltonian matrix is not exploited well, and the order of the computational amount becomes extremely large. To solve this problem, I developed a new infinite product expansion method and applied it to the Monte Carlo of the Kondo lattice model and the Kitaev model. This expansion has enabled us to reduce the computational complexity of the Monte Carlo method from O(N^3)/O(N^4) to O(N)/O(N^2) for a system size N, making it possible to speed up and scale up simulations of the Kitaev model and the Kondo lattice model. By increasing N, we will study novel topological phase transitions in three-dimensional Kitaev models and novel topological excitations in frustrated Kondo lattice models.