Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit

We consider the zero temperature behavior of dynamic response functions of 1D systems near edges of support in the momentum-energy plane (k,omega). The description of the singularities of dynamic response functions near an edge epsilon(k) is given by the effective Hamiltonian of a mobile impurity moving in a Luttinger liquid. For Galilean-invariant systems, we relate the parameters of such an effective Hamiltonian to the properties of the function epsilon(k). This allows us to express the exponents which characterize singular response functions of spinless bosonic or fermionic liquids in terms of epsilon(k) and Luttinger liquid parameters for any k. For an antiferromagnetic Heisenberg spin-1/2 chain in a zero magnetic field, SU(2) invariance fixes the exponents from purely phenomenological considerations.