AUTOCORRELATION FUNCTIONS FOR HERMITIAN MANY-BODY SYSTEMS - NECESSARY CONDITIONS

Brown [Phys. Rev. B 45, 10 809 (199 1)] points out an error made in an article on the dynamics of a Heisenberg model by Wysin and Bishop [Phys. Rev. B 42, 810 (1990)]. After correcting the error, he arrives at the conclusion that the dynamic structure in this model cannot be in the form of Lorentzians. We show that this conclusion represents an orthogonality condition of certain basis vectors that span Hilbert space. Hence, it is applicable to all Hermitian many-body models. Also, a simple model is provided to illustrate both the orthogonality and transformation ideas. They can be very useful in the dynamical studies of Hermitian many-particle systems.