Magnons versus free spinons in finite quantum frustrated antiferromagnets

We have investigated the validity of doping with a vacancy the J 1 – J 3 frustrated Heisenberg model on a finite square lattice as a way to test the existence of fractional spin excitations. Using a generalized t – J 1 – J 3 model we have computed the vacancy spectral functions in the self-consistent Born approximation. We have found that by including spiral fluctuations in the magnetic ground state, the spectral functions on finite systems agree very well with the unbiased exact ones. In contrast to the recent proposal that the quasiparticle weight reduction could be a signal of a spinon free excitation in finite systems, we have found strong evidence that such a reduction is due to the existence of spiral fluctuations.