Density matrix renormalisation group method and symmetries of the Hamiltonian

Substantial improvements in the computational effort in a density matrix re normalisation program can be made by utilising symmetries of the Hamiltonia n. Extra quantum numbers are always desirable to include in the calculation , since it allows the Hilbert space of the superblock to be refined. Since the speed of the calculation is approximately O(n(3)) in superblock states, the speed increase in targeting a specific total spin state can be conside rable. In this paper a new density matrix renormalisation algorithm is pres ented which conserves the total spin. The general procedure obtained works fbr any operator, even operators that do not commute with the Hamiltonian.