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

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 dwave 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 ≈ 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.

From underdoped to overdoped cuprates: two quantum phase transitions

“…Cluster generalization of DMFT [48,49,50,51] is necessary to study electron correlations in a two-dimensional CuO 2 layer where the nearest neighbor spin correlations require the momentum dependent self-energy. The cellular DMFT (CDMFT) method provides k-dependent self-energy and results in the phase diagrams that have features similar to the ones experimentally observed in cuprates [52,53,54,55,56]. Recently, the exact diagonalization version of CDMFT (CDMFT+ED) was used to study the electronic structure of the doped MottHubbard insulator [57,58].…”

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

“…As discussed in the literature before [9], the natural tendency of a finite oxygen band width is to delocalize and to destabilize the ZR singlets. Secondly, the pragmatic finding that a t-t -U 1BH-model with a significant value of t , captures basic physics of the cuprates and in particular their e-h asymmetry, cannot be accounted for in a strict ZR picture [26].…”

“…"half-filled" situation, are "charge-transfer" insulators [1,2]. This fact induces an experimentally observed asymmetry between hole (h)-and electron (e)-doping: while doped holes go onto O orbitals and may be bound to Cu spins to form "Zhang-Rice" singlets, doped electrons reside mainly on the Cu orbitals [3,4,5,6,7,8,9,10]. This is believed to be intimately related to the more extended stability of antiferromagnetic (AF) behavior as a function of electron doping compared to that of hole doping.…”

Pseudogap and Antiferromagnetic Correlations in the Hubbard Model

“…In the electron doped cuprates AF is more robust (persisting to ≈ 15% doping) [9] and the ARPES at small doping (≈ 5%) shows sharp quasiparticles at the zone edge and gap states elsewhere in the BZ [5,8]. In the Hubbard model, or the closely related t-J model, the electron-hole asymmetry can be captured by including a finite next-nearest neighbor hopping t ′ [10,11]. In this Letter we employ a reliable technique, the dynamical cluster approximation (DCA) [12,13], on relatively large clusters, to investigate the PG and single-particle spectra at small doping, the asymmetry between electron and hole-doped systems, and the role of AF correlations on the PG physics.…”