The thermodynamic limit of particle-hole form factors in the massless XXZ Heisenberg chain

We study the thermodynamic limit of the particle-hole form factors of the XXZ Heisenberg chain in the massless regime. We show that, in this limit, such form factors decrease as an explicitly computed power law in the system size. Moreover, each corresponding amplitude can be obtained as a product of a 'smooth' and a 'discrete' part: the former depends continuously on the rapidities of the particles and holes, whereas the latter has an additional explicit dependence on the set of integer numbers that label each excited state in the associated logarithmic Bethe equations. We also show that special form factors corresponding to zero-energy excitations lying on the Fermi surface decrease as a power law in the system size with the same critical exponents as in the long-distance asymptotic behavior of the related two-point correlation functions. The methods that we develop in this paper are rather general and can be applied to other massless integrable models associated with the six-vertex R-matrix and having determinant representations for their form factors.