Eur. Phys. J. Special Topics 188, 15-32 (2010)
https://doi.org/10.1140/epjst/e2010-01294-y

Regular Article

The 3-band Hubbard-model versus the 1-band model for the high-T_c cuprates: Pairing dynamics, superconductivity and the ground-state phase diagram

¹ Institute for Theoretical Physics, University of Würzburg, Am Hubland, 97074 Würzburg, Germany
² Centre de Physique Théorique, École Polytechnique, CNRS, 91128 Palaiseau Cedex, France
³ Institute of Theoretical and Computational Physics, Graz University of Technology, Petersgasse 16, 8010 Graz, Austria

Received: 14 July 2010
Revised: 12 August 2010
Published online: 11 October 2010

Abstract

One central challenge in high-T_c superconductivity (SC) is to derive a detailed understanding for the specific role of the Cu-d_x2-y2 and O-p_x,y orbital degrees of freedom. In most theoretical studies an effective one-band Hubbard (1BH) or t-J model has been used. Here, the physics is that of doping into a Mott-insulator, whereas the actual high-T_c cuprates are doped charge-transfer insulators. To shed light on the related question, where the material-dependent physics enters, we compare the competing magnetic and superconducting phases in the ground state, the single- and two-particle excitations and, in particular, the pairing interaction and its dynamics in the three-band Hubbard (3BH) and 1BH-models. Using a cluster embedding scheme, i.e. the variational cluster approach (VCA), we find which frequencies are relevant for pairing in the two models as a function of interaction strength and doping: in the 3BH-models the interaction in the low- to optimal-doping regime is dominated by retarded pairing due to low-energy spin fluctuations with surprisingly little influence of inter-band (p-d charge) fluctuations. On the other hand, in the 1BH-model, in addition a part comes from “high-energy” excited states (Hubbard band), which may be identified with a non-retarded contribution. We find these differences between a charge-transfer and a Mott insulator to be renormalized away for the ground-state phase diagram of the 3BH- and 1BH-models, which are in close overall agreement, i.e. are “universal”. On the other hand, we expect the differences - and thus, the material dependence to show up in the “non-universal” finite-T phase diagram (T_c-values).