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The exchange-correlation potential formalism previously introduced andapplied to the one-dimensional Hubbard model has been extended to spin systemsand applied to the case of the one-dimensional antiferromagneticspin$-\frac{1}{2}$ Heisenberg model. Within the spin exchange-correlationpotential formulation, a new sum rule for spin-systems is derived. Theexchange-correlation potential for the Heisenberg model is extrapolated fromexact diagonalization results of small antiferromagnetic Heisenberg clusters.This procedure is also employed to revisit and computationally improve theprevious investigation of the exchange-correlation potential of the half-filledHubbard model, which was based on the exchange-correlation potential of thedimer. Numerical comparisons with exact benchmark calculations for both theHeisenberg and the Hubbard models indicate that, starting from theexchange-correlation potential of a finite cluster, the extrapolation procedureyields a one-particle spectral function with favorable accuracy at a relativelylow computational cost. In addition, a comparison between the ground stateenergies for the one-dimensional Hubbard and Heisenberg models displays how thewell known similarity in behavior of the two models at large interactionsmanifests within the exchange-correlation potential formalism.

Dynamical exchange-correlation potential formalism for spin-$\frac{1}{2}$ Heisenberg and Hubbard chains: the antiferromagnetic/half-filled case