Dynamical transition from triplets to spinon excitations : A series expansion study of the J 1 - J 2 - d spin - 1 2 chain

We study the spin-1/2 Heisenberg chain with alternating nearest neighbor interactions J1(11d) and J1(1 2d) and a uniform second neighbor interaction J25y(12d) by series expansions around the limit of decoupled dimers (d51). By extrapolating to d50 and tuning y, we study the critical point separating the powerlaw and spontaneously dimerized phases of the spin-1/2 antiferromagnet. We then focus on the disorder line y50.5, 0<d<1, where the ground states are known exactly. We calculate the triplet excitation spectrum, their spectral weights, and wave vector dependent static susceptibility along this line. It is well known that as d →0, the spin gap is still nonzero but the triplets are replaced by spinons as the elementary excitations. We study this dynamical transition by analyzing the series for the spectral weight and the static susceptibility. In particular, we show that the spectral weight for the triplets vanishes and the static spin susceptibility changes from a simple pole at imaginary wave vectors to a branch cut at the transition. @S0163-1829~99!00615-3#