Threshold singularities in the dynamic response of gapless integrable models

We develop a method of an asymptotically exact treatment of threshold singularities in dynamic response functions of gapless integrable models. The method utilizes the integrability to recast the original problem in terms of the low-energy properties of a certain deformed Hamiltonian. The deformed Hamiltonian is local, hence it can be analysed using the conventional field theory methods. We apply the technique to spinless fermions on a lattice with nearest-neighbors repulsion, and evaluate the exponent characterizing the threshold singularity in the dynamic structure factor.