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

We investigate the influence of biquadratic exchange interactions on the low-lying excitations of a $S=\frac{1}{2}$ ladder using perturbation theory, numerical diagonalization of finite systems, and exact results for ladders with matrix product ground states. We consider in particular the combination of biquadratic exchange interactions corresponding to ring exchange on the basic ladder plaquette. We find that a moderate amount of ring exchange reduces the spin gap substantially and makes equal bilinear exchange on legs and rungs consistent with experimentally observed spectra.