Dynamical transition from triplets to spinon excitations:: A series expansion study of the J1-J2-δ spin-1/2 chain

We study the spin-1/2 Heisenberg chain with alternating nearest neighbor interactions J(1)(1 + delta) and J(1)(1 - delta) and a uniform second neighbor interaction J(2) = y(1 - delta) by series expansions around the Limit of decoupled dimers (delta = 1). By extrapolating to delta = 0 and tuning y, we study the critical point separating the power-law and spontaneously dimerized phases of the spin-1/2 antiferromagnet. We then focus on the disorder line y = 0.5, 0 less than or equal to delta less than or equal to 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 delta --> 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].