Spin and charge fluctuations in the two-band Hubbard model
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THE EUROPEAN PHYSICAL JOURNAL B
Regular Article
Spin and charge fluctuations in the two-band Hubbard model Alexei Sherman a Institute of Physics, University of Tartu, 1 W. Ostwaldi Street, 50411 Tartu, Estonia
Received 30 April 2020 / Received in final form 26 June 2020 Published online 2 September 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. A model of CuO2 planes of cuprate perovskites, containing dx2 −y2 copper orbitals and symmetric combinations of oxygen pσ orbitals, is investigated using the strong coupling diagram technique. This approach allows one to take into account the interactions of carriers with spin and charge fluctuations of all ranges. Derived equations for Green’s function are self-consistently solved for the set of parameters corresponding to hole- and electron-doped cuprates. It is shown that the mentioned interactions lead to the appearance of spin polarons – bound states of carriers with spin excitations, which show themselves as sharp peaks of the density of states and spectral functions at the Fermi level. Hole and electron doping are strongly asymmetric. This, in particular, manifests itself in the antiferromagnetic response for the electron-doped case and in an incommensurate magnetic ordering for hole doping. In the latter case, the incommensurability parameter grows with doping. The double occupancy shows that the electron-doped system retains strong correlations up to the concentration 0.23, while for hole doping the correlations decay rapidly. These results are in agreement with experimental observations in cuprates.
1 Introduction The three-band Hubbard model contains a minimal set of states, which is necessary for the description of CuO2 planes of cuprate high-Tc superconductors – a copper 3dx2 −y2 and two oxygen 2pσ orbitals per unit cell [1–3]. Previously, the model was investigated by different methods including exact diagonalization of small clusters [4,5], Monte Carlo simulations [6,7], the dynamic cluster approximation [8], dynamic mean-field approximation (DMFT) [9–12], variational cluster approach [13], densitymatrix-renormalization-group calculations [14] and the strong coupling diagram technique (SCDT) using two lowest orders of the series expansion [15]. These works have shown that the model exhibits a number of the basic magnetic and single-particle spectral properties that are seen in the cuprates. They demonstrated also that the lowfrequency part of the model spectrum has some similarity with the spectrum of the one-band Hubbard model. The mentioned works either did not consider interactions of carriers with spin and charge fluctuations or took into account only their short-range part. In the present work, we take into consideration the fluctuations of all ranges using the SCDT [16–20]. In this approach, Green’s functions are calculated using series expansions in powers of the carrier intersite hopping term of the Hamiltonian. Terms of the series are products of hopping constants and on-
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