Reducing Computational Time of Quantum Diagonalization Calculation for 2-Dimensional Strongly Correlated Systems

We reduce the computational time of the quantum Monte Carlo diagonalization (QMCD) (in De Raedt and von der Linden, Phys. Rev. B 45:8787, 1992 ) calculation for 2-dimensional strongly correlated systems by using several methods including symmetry operations. First, we subdivide each lattice into spin-up and spin-down lattices separately, thus allowing a bi-partite lattice. A valid base is then obtained from stacking up an up-spin configuration on top of a down-spin configuration. As a consequence, the memory space to be used in saving the trial basis reduces substantially. Secondly, we record the matrix elements of a Hamiltonian in a look-up table when making basis set. Thus we avoid the repeated calculation of the matrix elements of the Hamiltonian during the diagonalization process. Thirdly, by applying symmetry operations to the basis set, the original basis is transformed to a new basis, whose elements are the eigenvectors of the symmetry operations. The ground state wavefunction is constructed from the elements of symmetric (bonding state) basis set. As a result, the total number of bases involved in the quantum Monte Carlo diagonalization calculation is reduced significantly by using symmetry operations.