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We study the thermodynamic limit of the particle-hole form factors of the XXZHeisenberg chain in the massless regime. We show that, in this limit, such formfactors decrease as an explicitly computed power-law in the system-size.Moreover, the corresponding amplitudes can be obtained as a product of a"smooth" and a "discrete" part: the former depends continuously on therapidities of the particles and holes, whereas the latter has an additionalexplicit dependence on the set of integer numbers that label each excited statein the associated logarithmic Bethe equations. We also show that special formfactors 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 we develop in this article are rather general and can beapplied to other massless integrable models associated to the six-vertexR-matrix and having determinant representations for their form factors.

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