Exact and fast calculation for two-dimensional correlated electron systems: application to the Hubbard model

The two dimensional systems of correlated electrons is solved by using the quantum Monte Carlo diagonalization (QMCD). 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 model. The computational capability of the QMCD method can be improved by using bitwise Boolean operations, by reducing state space based on symmetry properties, and by effectively transforming the trial state. Some of the results for the Hubbard model showed that the time complexities are much lower when more symmetries are used. The approach is rerestricted by the memory capacity to keep the trial state, and it finds the exact solutions for a problem with order of 109-state bases when using the internal memory of a single PC.