Abstract
We have performed exact calculations of two-spin and four-spin time-correlation functions, such as 〈Siz(t)Sjz〉 and 〈Siz(t)Sj+(t)SkzSl−〉, for finite linear chains with periodic boundary conditions containing as many as ten spin-½ particles coupled by a nearest-neighbor Heisenberg exchange interaction. Previous workers have computed thermodynamic properties of finite linear chains, but this to our knowledge is the first calculation of time-dependent properties, which requires the eigenfunctions as well as eigenvalues. Determination of the correlation functions enables us to compute the variation of magnetic-resonance linewidth with frequency in a linear-chain salt such as Cu(NH3)4SO4·H2O by applying the methods of Kubo and Tomita. Values of linewidth computed with our exact correlation functions give very much better agreement with Rogers' experimental values for Cu(NH3)4SO4·H2O than the usual Gaussian approximation. We also show results for the simple two-spin correlation function, such as measured by inelastic neutron scattering. Its frequency transform is non-Gaussian, showing a steep rise near zero frequency.
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