On singularities of dynamic response functions in the massless regime of the XXZ spin-1/2 chain

Abstract

This work extracts, by means of an exact analysis, the singular behavior of the dynamical response functions—the Fourier transforms of dynamical two-point functions—in the vicinity of the various excitation thresholds in the massless regime of the XXZ spin-1/2 chain. The analysis yields the edge exponents and associated amplitudes that describe the local behavior of the response function near a threshold. The singular behavior is derived starting from first principles considerations: the method of analysis does not rely, at any stage, on some hypothetical correspondence with a field theory or other phenomenological approaches. The analysis builds on the massless form factor expansion for the response functions of the XXZ chain obtained recently by the author. It confirms the non-linear Luttinger based predictions relative to the power-law behavior and of the associated edge exponents that arise in the vicinity of the dispersion relation of one massive excitation (hole, particle, or bound state). In addition, the present analysis shows that due to the lack of strict convexity of the particle dispersion relation and due to the presence of slow velocity branches of the bound states, there exist excitation thresholds with a different structure of edge exponents. These originate from multi-particle/hole/bound state excitations maximizing the energy at fixed momentum.