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An infinite set of sum rules is derived for the dynamics of one-dimensional quantum spin systems. They are employed to derive valuable information on the spectral-weight distribution in the T=0 dynamic structure factor Sμμ(q, ω). Applications are presented for various special cases of the nearest-neighbor XXZ model, including cases with a discrete excitation spectrum and cases with a continuous spectrum. For the S=1/2 XY-Heisenberg antiferromagnet, an analytic expression for Szz(q, ω) is conjectured which satisfies the infinite set of sum rules. In the XY limit this expression is identical to the known exact result. A similar conjecture applied to the isotropic Heisenberg antiferromagnet with arbitrary spin quantum number S illustrates how the continuous spectrum of the quantum antiferromagnet collapses into a discrete branch of antiferromagnetic spin waves in the classical limit S→∞.
Gerhard Müller. Sum rules in the dynamics of quantum spin chains. Phys. Rev. B 26 (1982), 1311-1320. Available at: http://dx.doi.org/10.1103/PhysRevB.26.1311