Density Matrix Renormalisation Group Method and Symmetries of the Hamiltonian

Substantial improvements in the computational effort in a density matrix renormalisation program can be made by utilising symmetries of the Hamiltonian. Extra quantum numbers are always desirable to include in the calculation, since it allows the Hubert space of the superblock to be refined. Since the speed of the calculation is approximately O(n³) in superblock states, the speed increase in targeting a specific total spin state can be considerable. In this paper a new density matrix renormalisation algorithm is presented which conserves the total spin. The general procedure obtained works for any operator, even operators that do not commute with the Hamiltonian.