The half - filled Hubbard chain in the Composite Operator Method : A comparison with Bethe Ansatz

– The one-dimensional Hubbard model at half-filling is studied in the framework of the Composite Operator Method using a static approximation. A solution characterized by strong antiferromagnetic correlations and a gap for any nonzero on-site interaction U is found. The corresponding ground-state energy, double occupancy and specific heat are in excellent agreement with those obtained within the Bethe Ansatz. These results show that the Composite Operator Method is an appropriate framework for the half-filled Hubbard chain and can be applied to evaluate properties, like the correlation functions, which cannot be obtained by means of the Bethe Ansatz, except for some limiting cases. Introduction. – New materials whose physics is dominated by electron correlations in narrow energy bands are actually a challenge for solid state physicists. The treatment of such systems is not trivial due to the competition between itinerant and localized behaviour of the electrons in these bands. The Hubbard Hamiltonian [1] is regarded as the simplest model which can give us the basic understanding of the effects of strong electronic correlations. In particular, its one-dimensional (1D) version is interesting for several reasons. On the one hand it is exactly integrable, by means of the Bethe Ansatz [2]. On the other, it could be applied to study real quasi-1D systems like the KCP and T T F − T CN Q salts [3], the doped spin Peierls chains [4] and the Cu-O chains of the high-T c superconductors, whose underlying physics is directly related to the low-dimensionality of the system. By using the Bethe Ansatz and following a method developed by Yang [5], Lieb and Wu evaluated exactly some ground-state properties of the 1D Hubbard model at half filling [6]. Two years later, the spin and charge excitation spectra were obtained, also within the Bethe Ansatz, by Ovchinnikov [7]. For arbitrary electron density, the Bethe Ansatz coupled integral