Effects of biquadratic exchange on the spectrum of elementary excitations in spin ladders

We investigate the influence of biquadratic exchange interactions on the lo w-lying excitations of a S = 1/2 ladder using perturbation theory, numerica l diagonalization of finite systems, and exact results for ladders with mat rix product ground states. We consider in particular the combination of biq uadratic exchange interactions corresponding to ring exchange on the basic ladder plaquette. We find that a moderate amount of ring exchange reduces t he spin gap substantially and makes equal bilinear exchange on legs and run gs consistent with experimentally observed spectra. [S0163-1829(99)05425-9] .