Matrix Elements of Observables in Interacting Integrable Systems

We study the matrix elements of local operators in the eigenstates of an interacting integrable Hamiltonian (the spin-1/2 XXZ chain) at the center of the spectrum, and contrast their behavior with that of quantum chaotic systems. For the diagonal matrix elements, we show evidence that the support does not vanish with increasing system size, while the average eigenstate to eigenstate fluctuations vanish in a power law fashion. For the off-diagonal matrix elements, we show that their distribution is close to (but not quite) log-normal, and that their variance is a well-defined function of ω=E α −E β ({E α } are the eigenenergies) proportional to 1/D, where D is the Hilbert space dimension.