CALCULATION OF THE SINGLET-TRIPLET GAP OF THE ANTIFERROMAGNETIC HEISENBERG-MODEL ON A LADDER

The ground-state energy and the singlet-triplet energy pp of the antif erromagnetic Heisenberg model on a ladder is investigated using a mean -field theory and the density-matrix renormalization group. Spin-wave theory shows that the corrections to the local magnetization are infin ite. This indicates that no long-range order occurs in this system. A flux-phase state is used to calculate the energy pp as a function of t he transverse coupling, J(perpendicular-to), in the ladder. It is foun d that the gap is linear in J(perpendicular-to) for J(perpendicular-to ) much greater than 1 and goes to zero for J(perpendicular-to) --> 0. The mean-field theory agrees well with the numerical results.