Spectral properties of the large-negative-U Hubbard model

Abstract

Using the formalism introduced by Harris and Lange ͓Phys. Rev. 157, 295 ͑1967͔͒ explicit expressions for partial sum rules of the individual Hubbard bands in the large-negative-U limit are derived. The one-particle spectrum, optical spectrum, as well as charge-and spin-response functions are considered. The approach gives a transparent description of the main features of these spectra. The main sum rules depend on only two independent nearest-neighbor expectation values which are estimated in the ground state using numerical calculations, exact results, and linear-spin-wave theory. Simple expressions for the intensities of the upper and lower Hubbard bands in the optical conductivity show that this spectrum is extremely sensitive on details of the ground state. The charge-density wave and superconducting phases are clearly distinguishable and even the transition to the broken-symmetry state may have a detectable influence on the conductivity.

Beyond the Hubbard-I solution with a one-pole self-energy at half-filling within the moment approach

“…We comment here that the band-narrowing factor, B(T ), in general, is k-dependent. This dependence has been explicitly been shown recently to be important by Eskes and Oleś [11].…”

“…Eqs. (11) are nothing else that the solutions given by Nolting [6] by solving the four unknown α i ( k) and ω i ( k), with i = 1, 2. We have regained Nolting's solutions in a much easier way, starting from the self-energy, while Nolting does it from the Green function itself.…”

“…As our solutions given by Eqs. (11) satisfy the first four sum rules or moments, our Green function is beyond the Hubbard-I solution [8] and as a consequence we have an improved solution [7]. The drawback of the Hubbard-I solution, i.e., a gap for any value of the interaction, was pointed out by Laura Roth [9] many years ago.…”

Evolution of one-particle and double-occupied Green functions for the Hubbard model, with interaction, at half-filling with lifetime effects within the moment approach

“…We call the attention to Ref. [25] where the authors point out to the fact that the k-dependence has to be included in B( k). A recent calculation by Kirchhofer [26] is performed at the mean field level for the k-dependence of the band narrowing factor, when the two Hubbard bands are separated.…”

The Mott metal - insulator transition in the two-dimensional Hubbard model at half-filling with lifetime effects within the moment approach

“…We call the attention to Ref. [18] where the authors point out to the fact that the k-dependence has to be included in B( k). However, they study the negative Hubbard model in the strong coupling limit and in this limit we have a well developed correlation gap, anyway.…”