A unique feature of some simple many body quantum spin systems

Dynamical correlations in simple quantum spin models can be conveniently studied via the continued fraction formalism in which the Laplace transformed dynamical two-point correlation can be written as C(z) = 1/(z + Δ₁/(z + Δ₂/(z + to ∞))), where Δ_n's are functions of static correlations. Very often, for systems without any natural dominant characteristic frequencies, as n increases, Δ_n ≊ κn^α, α=0 or 1, κ being some constant, for large n for simple quantum spin systems. It is suggested that this property of Δ_n's could be related to some underlying "nearly noninteracting fermionic nature" of these quantum spin systems.