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The dynamical spin structure factor is computed within a variationalframework to study the one-dimensional $J_1-J_2$ Heisenberg model. Startingfrom Gutzwiller-projected fermionic wave functions, the low-energy spectrum isconstructed from two-spinon excitations. The direct comparison with Lanczoscalculations on small clusters demonstrates the excellent description of bothgapless and gapped (dimerized) phases, also including incommensurate structuresfor $J_2/J_1>0.5$. Calculations on large clusters show how the intensityevolves when increasing the frustrating ratio and give an unprecedentedaccurate characterization of the dynamical properties of (non-integrable)frustrated spin models.

Dynamical structure factor of the $J_1-J_2$ Heisenberg model in one dimension: the variational Monte Carlo approach