Perturbation theory of low-dimensional quantum liquids. II. Operator description of Virasoro algebras in integrable systems

We show that the recently developed pseudoparticle-operator algebra which generates the low-energy Hamiltonian eigenstates of multicomponent integrable systems with contact interactions also provides a natural operator representation for the Virasoro algebras associated with the conformal-invariant character of the low-energy spectrum of these models. Studying explicitly the Hubbard chain in a nonzero chemical potential and external magnetic field, we establish that the pseudoparticle-perturbation theory provides a correct starting point for the construction of a suitable critical-point Hamiltonian. We derive explicit expressions in terms of pseudoparticle operators for the generators of the Virasoro algebras and the energy-momentum tensor, describe the conformal-invariant character of the critical point from the point of view of the response to curvature of the two-dimensional space time, and discuss the relation to Kac-Moody algebras and dynamical separation.