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The spectral functions of the one-band half-filled 1D Hubbard chain arecalculated using the exchange-correlation potential formalism developedrecently. The exchange-correlation potential is adopted from the exactpotential derived from the Hubbard dimer. Within an approximation in which thefull Green function is replaced by a non-interacting one, the spectralfunctions can be calculated analytically. Despite the simplicity of theapproximation, the resulting spectra are in favorable agreement with the moreaccurate results obtained from the dynamic density-matrix renormalization groupmethod. In particular, the calculated band gap as a function of $U$ is in closeagreement with the exact gap obtained from the Bethe ansatz. In addition, theformal general solution to the equation of motion of the Green function ispresented and the difference between the traditional self-energy approach andthe exchange-correlation potential formalism is also discussed and elaborated.A simplified Holstein Hamiltonian is considered to further illustrate thegeneral form of the exchange-correlation potential.

Spectral functions of the half-filled 1D Hubbard chain within the exchange-correlation potential formalism