Physics of cuprates with the two-band Hubbard model - The validity of the one-band Hubbard model

TL;DR

This study uses the two-band Hubbard model to analyze cuprate properties, finding that a single-band model with appropriate parameters can capture essential physics but not all high-energy details.

Contribution

It demonstrates that the single-band Hubbard model with a significant t' term can replicate key low-energy phenomena of the two-band model in cuprates.

Findings

The phase diagram shows electron-hole asymmetry consistent with experiments.

Similar low-energy physics are captured by the single-band model with t'/t ≈ 0.3.

The single-band model is inadequate for high-energy properties above 0.5 eV.

Abstract

We calculate the properties of the two-band Hubbard model using the Dynamical Cluster Approximation. The phase diagram resembles the generic phase diagram of the cuprates, showing a strong asymmetry with respect to electron and hole doped regimes, in agreement with experiment. Asymmetric features are also seen in one-particle spectral functions and in the charge, spin and d-wave pairing susceptibility functions. We address the possible reduction of the two-band model to a low-energy single-band one, as it was suggested by Zhang and Rice. Comparing the two-band Hubbard model properties with the single-band Hubbard model ones, we have found similar low-energy physics provided that the next-nearest-neighbor hopping term t' has a significant value ($t'/t \approx 0.3$). The parameter t' is the main culprit for the electron-hole asymmetry. However, a significant value of t' cannot be provided in a strict Zhang and Rice picture where the extra holes added into the system bind to the existing Cu holes forming local singlets. We notice that by considering approximate singlet states, such as plaquette ones, reasonable values of t', which capture qualitatively the physics of the two-band model can be obtained. We conclude that a single-band t-t'-U Hubbard model captures the basic physics of the cuprates concerning superconductivity, antiferromagnetism, pseudogap and electron-hole asymmetry, but is not suitable for a quantitative analysis or to describe physical properties involving energy scales larger than about 0.5 eV.