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The two particle-hole pairs contribution to the dynamic correlation functions of quantum integrable models

We consider the problem of computing dynamic correlation functions of quantum integrable models employing the thermodynamic form-factor approach. Specifically, we focus on correlations of local operators that conserve the number of particles and consider the 2-particle-hole contribution to their two-point functions. With the method developed being generally applicable to any finite energy and entropy state, our primary focus is on the thermal states. To exemplify this approach, we chose the Lieb-Liniger model and study the leading contribution from 2-particle-hole excitations at small momenta to the dynamic density-density correlation function. We also consider analogous contributions to two-point functions of higher local conserved densities and currents present in integrable theories.