A technique for studying spin-1/2 lattices, based on the properties of the symmetric group ${\mathrm{S}}_{\mathrm{N}}$, is presented. It is shown that the symmetric-group approach, applied to the Heisenberg Hamiltonian, leads to efficient diagonalization algorithms. Some examples of calculations for the lowest singlet and triplet states of the 2×L isotropic antiferromagnetic Heisenberg ladders are compared with results in the literature. For the singlet-triplet gap we have obtained, by extrapolation to the bulk limit, the values 0.498 949 and 0.499 545 for a polynomial and an exponential fit, respectively.

DOI:https://doi.org/10.1103/PhysRevB.55.8287