The thermodynamic limit of particle–hole form factors in the masslessXXZ Heisenberg chain

Abstract

We study the thermodynamic limit of the particle–hole form factors of theXXZ Heisenberg chain in the massless regime. We show that, in this limit, such form factorsdecrease as an explicitly computed power law in the system size. Moreover, eachcorresponding 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 thelatter has an additional explicit dependence on the set of integer numbers that label eachexcited state in the associated logarithmic Bethe equations. We also show that specialform factors corresponding to zero-energy excitations lying on the Fermi surfacedecrease as a power law in the system size with the same critical exponents asin the long-distance asymptotic behavior of the related two-point correlationfunctions. The methods that we develop in this paper are rather general and canbe applied to other massless integrable models associated with the six-vertexR-matrix and having determinant representations for their form factors.