Exact and Fast Calculation for Two-Dimensional Correlated Electron Systems: Application to the Hubbard Model

Abstract

The quantum Monte Carlo diagonalization (QMCD) is introduced as a computational method to solve the 2-D systems of correlated electrons exactly. The QMCD is based on a variational method, in which the solution approaches the optimal eigenvalue and eigenstate of a huge matrix originating from the Hubbard or t-J model. It is difficult, however, to apply this method to large systems because the number of quantum states increases rapidly as the system size grows. We improve the computational capability of the QMCD significantly by using bitwise Boolean operations, by reducing state space based on symmetry properties, and by effectively transforming the trial state. Some of our results for the Hubbard model are described. Our approach is only restricted by the memory capacity to keep the trial state. It finds exact solutions fast even for a problem with order of 10^9-state bases when using the internal memory of a single PC.