Excitation spectrum of Heisenberg spin ladders

Heisenberg antiferromagnetic spin ‘‘ladders’’ (two coupled spin chains) are low-dimensional magnetic systems which for S=1/2 interpolate between half-integer-spin chains, when the chains are decoupled, and effective integer-spin one-dimensional chains in the strong-coupling limit. The spin-1/2 ladder may be realized in nature by vanadyl pyrophosphate, (VO)₂P₂O₇. In this paper we apply strong-coupling perturbation theory, spin-wave theory, Lanczos techniques, and a Monte Carlo method to determine the ground-state energy and the low-lying excitation spectrum of the ladder. We find evidence of a nonzero spin gap for all interchain couplings J_⊥>0. A band of spin-triplet excitations above the gap is also analyzed. These excitations are unusual for an antiferromagnet, since their long-wavelength dispersion relation behaves as (k-k₀)² (in the strong-coupling limit J_⊥≫J, where J is the in-chain antiferromagnetic coupling). Their band is folded, with a minimum energy at k₀=π, and a maximum between k₁=π/2 (for J_⊥=0) and 0 (for J_⊥=∞). We also give numerical results for the dynamical structure factor S(q,ω), which can be determined in neutron scattering experiments. Finally, possible experimental techniques for studying the excitation spectrum are discussed.