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Register a new userPhase diagram and single-particle spectrum of CuO$_2$ layers within a variational cluster approach to the 3-band Hubbard model
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We carry out a detailed numerical study of the three-band Hubbard model in the underdoped region both in the hole- as well as in the electron-doped case by means of the variational cluster approach. Both the phase diagram and the low-energy single-particle spectrum are very similar to recent results for the single-band Hubbard model with next-nearest-neighbor hoppings. In particular, we obtain a mixed antiferromagnetic+superconducting phase at low doping with a first-order transition to a pure superconducting phase accompanied by phase separation. In the single-particle spectrum a clear Zhang-Rice singlet band with an incoherent and a coherent part can be seen, in which holes enter upon doping around $(pi/2,pi/2)$. The latter is very similar to the coherent quasi-particle band crossing the Fermi surface in the single-band model. Doped electrons go instead into the upper Hubbard band, first filling the regions of the Brillouin zone around $(pi,0)$. This fact can be related to the enhanced robustness of the antiferromagnetic phase as a function of electron doping compared to hole doping.
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Using the variational cluster approach (VCA), we study the transition from the antiferromagnetic to the superconducting phase of the two-dimensional Hubbard model at zero temperature. Our calculations are based on a new method to evaluate the VCA grand potential which employs a modified Lanczos algorithm and avoids integrations over the real or imaginary frequency axis. Thereby, very accurate results are possible for cluster sizes not accessible to full diagonalization. This is important for an improved treatment of short-range correlations, including correlations between Cooper pairs in particular. We investigate the cluster-size dependence of the phase-separation tendency that has been proposed recently on the basis of calculations for smaller clusters. It is shown that the energy barrier driving the phase separation decreases with increasing cluster size. This supports the conjecture that the ground state exhibits microscopic inhomogeneities rather than macroscopic phase separation. The evolution of the single-particle spectum as a function of doping is studied in addtion and the relevance of our results for experimental findings is pointed out.
We determine the ground-state phase diagram of the three-band Hubbard model across a range of model parameters using density matrix embedding theory. We study the atomic-scale nature of the antiferromagnetic (AFM) and superconducting (SC) orders, explicitly including the oxygen degrees of freedom. All parametrizations of the model display AFM and SC phases, but the decay of AFM order with doping is too slow compared to the experimental phase diagram, and further, coexistence of AFM and SC orders occurs in all parameter sets. The local magnetic moment localizes entirely at the copper sites. The magnetic phase diagram is particularly sensitive to $Delta_{pd}$ and $t_{pp}$, and existing estimates of the charge transfer gap $Delta_{pd}$ appear too large in so-called minimal model parametrizations. The electron-doped side of the phase diagram is qualitatively distinct from hole-doped side and we find an unusual two-peak structure in the SC in the full model parametrization. Examining the SC order at the atomic scale, within the larger scale $d_{x^2 - y^2}$-wave SC pairing order between Cu-Cu and O-O, we also observe a local $p_{x (y)}$ [or $d_{xz (yz)}$]-symmetry modulation of the pair density on the Cu-O bonds. Our work highlights some of the features that arise in a three-band versus one-band picture, the role of the oxygen degrees of freedom in new kinds of atomic-scale SC orders, and the necessity of re-evaluating current parametrizations of the three-band Hubbard model.
The interplay between the Kondo effect and magnetic ordering driven by the Ruderman-Kittel-Kasuya-Yosida interaction is studied within the two-dimensional Hubbard-Kondo lattice model. In addition to the antiferromagnetic exchange interaction, $J_perp$, between the localized and the conduction electrons, this model also contains the local repulsion, $U$, between the conduction electrons. We use variational cluster approximation to investigate the competition between the antiferromagnetic phase, the Kondo singlet phase, and a ferrimagnetic phase on square lattice. At half-filling, the Neel antiferromagnetic phase dominates from small to moderate $J_perp$ and $UJ_perp$, and the Kondo singlet elsewhere. Sufficiently away from half-filling, the antiferromagnetic phase first gives way to a ferrimagnetic phase (in which the localized spins order ferromagnetically, and the conduction electrons do likewise, but the two mutually align antiferromagnetically), and then to the Kondo singlet phase.
We applied the Recurrent Variational Approach to the two-leg Hubbard ladder. At half-filling, our variational Ansatz was a generalization of the resonating valence bond state. At finite doping, hole pairs were allowed to move in the resonating valence bond background. The results obtained by the Recurrent Variational Approach were compared with results from Density Matrix Renormalization Group.
We consider the orbitally degenerate 3-band Hubbard model with on-site interactions which favor low spin and low orbital angular momentum using standard second order perturbation theory in the large Hubbard-U limit. At even integer filling this model is a Mott insulator with a non-degenerate ground state that allows for a simple description of particle-hole excitations as well as gapped spin and orbital modes. We find that the Mott gap is generally indirect and that the single particle spectrum at low doping reappears close to even filling but rescaled by a factor 2/3 or 1/3. The model captures the basic phenomenology of the Mott insulating and metallic fullerides AxC60. This includes the existence of a smaller spin gap and larger charge gap at even integer filling, the fact that odd integer stoichiometries are generally metallic while even are insulating, as well as the rapid suppression of the density of states and superconducting transition temperatures with doping away from x=3.
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