Elementary excitations in the gapped phase of a frustrated S=1/2 spin ladder: from spinons to the Haldane triplet

We use the variational matrix-product ansatz to study elementary excitations in the S = 1/2 ladder with additional diagonal coupling, equivalent to a single S = 1/2 chain with alternating exchange and next-nearest-neighbour interaction. In the absence of alternation, the elementary excitation consists of two free S = 1/2 particles ('spinons') which are solitons in the dimer order. When the nearest-neighbour exchange alternates, the 'spinons' are confined into one S = 1 excitation which is a soliton in the generalized string order. The variational results are found to be in qualitative agreement with the exact-diagonalization data for 24 spins. We argue that such an approach gives a reasonably good description over a wide range of the model parameters.