The t-J model has been proposed to describe the physics of copper oxide planes in high-temperature superconductors. A real-space quantum renormalization-group method is developed in order to study the t-J Hamiltonian in a square lattice. The zero-temperature phase diagram is analysed for electron concentrations near the half-filled band and ratio J/t. A critical line is found that separates two distinct regions: one of a gas of holes in an antiferromagnetic background, and the other consisting of a phase in which holes segregate into a hole-rich and a pure antiferromagnetic region, as demonstrated by chemical-potential eigenvalue calculations near the phase attractor. The results are close to the experimental observations.
The t-J model has been proposed to describe the physics of copper oxide planes in high-temperature superconductors. A real-space quantum renormalization-group method is developed in order to study the t-J Hamiltonian in a square lattice. The zero-temperature phase diagram is analysed for electron concentrations near the half-filled band and ratio J/t. A critical line is found that separates two distinct regions: one of a gas of holes in an antiferromagnetic background, and the other consisting of a phase in which holes segregate into a hole-rich and a pure antiferromagnetic region, as demonstrated by chemical-potential eigenvalue calculations near the phase attractor. The results are close to the experimental observations.
A systematic study is made of the t-J model as a working model for copper oxide high-Tc superconductors. The main focus is on the near-half- filling region (low hole concentrations) relevant to these materials. The theory of the magnetic polaron, which is a charge carrier traveling in an antiferromagnetic matrix, and the theory of antiferromagnetic ordering are discussed in a unified framework. The spin liquid state beyond the antiferromagnetic phase is examined. The Hamiltonian parameters – hole concentration phase diagram for the model is described and compared with that for the Hubbard model in the strong correlation limit. Two extensions of the t-J model, the t-t'-J model and the three-center interaction model, are discussed. Mostly analityc strong correlation techniques are employed in this review.
We carry out a systematic study of collective spin and charge excitations for the canonical single-band Hubbard, t–J–U, and t–J models of high-temperature copper-oxide superconductors, both on electron- and hole-doped side of the phase diagram. A~recently developed variational wave function approach, combined with the expansion in the inverse number of fermionic flavors, is employed. All three models exhibit a substantial electron–hole asymmetry of magnetic excitations, with a robust paramagnon emerging for hole-doping, in agreement with available resonant inelastic X-ray scattering data for the cuprates. The t–J model yields additional high-energy peak in the magnetic spectrum that is not unambiguously identified in spectroscopy. For all considered Hamiltonians, the dynamical charge susceptibility contains a coherent mode for both hole- and electron doping, with overall bandwidth renormalization controlled by the on-site Coulomb repulsion. Away from the strong-coupling limit, the antiferromagnetic ordering tendency is more pronounced on the electron-doped side of the phase diagram.
A generalized t-J Hamiltonian is analyzed within the framework of a quantum real-space renormalization group. Besides the usual hopping (t), exchange (J), and chemical-potential (\ensuremath{\mu}) terms, the Hamiltonian contains a nearest-neighbor charge interaction term and is invariant under the renormalization. The finite-temperature phase diagram of the d=2 and d=3 model is calculated in the full range of the parameters. Our results show that many of the critical properties of the La- and Y-based high-Tc superconductors can be explained by the present model.
Phase diagram of the Hubbard-Holstein model in the coexistence of electron-electron and electron-phonon interactions has been theoretically obtained with the density-matrix renormalization group method for one-dimensional systems, where an improved warm-up (the recursive sweep) procedure has enabled us to calculate various correlation functions. We have examined the cases of (i) the systems half-filled by electrons for the full parameter space spanned by the electron-electron and electron-phonon coupling constants and the phonon frequency, (ii) non-half-filled system, and (iii) trestle lattice. For (i), we have detected a region where both the charge and on-site pairing correlations decay with power laws in real space, which suggests a metallic behavior. While pairing correlations are not dominant in (i), we have found that they become dominant as the system is doped in (ii) or as the electronic band structure is modified (with a broken electron-hole symmetry) in (iii) in certain parameter regions.
The authors have used an exact diagonalization technique to explore the ground-state phase diagram of the two-dimensional Holstein-t-J model near half filling. The nature of the ground state is analysed, calculating self consistently the local lattice distortions, on-site spin and charge densities, as well as the magnetic structure form factor. They demonstrate that doped holes tend to form hole-polaron or bipolaron states. Compared to that in the uncorrelated model (spinless fermions), the critical electron-phonon coupling strength for the self-trapping transition of the doped charge carriers is considerably reduced by the antiferromagnetic exchange interaction. The relevance to the cuprate superconductors is discussed.
High-temperature superconductivity in copper oxides (cuprates, e.g. La2−xSrxCuO4, YBa2Cu3O6+δ or Bi2Sr2CaCu2O8+δ) remains among the most spectacular phenomena in condensed matter physics. Since its discovery in 1986, an enormous number (∼ 105) of papers on the subject have appeared. So far, there is no single, commonly accepted theory of high-temperature superconductivity. However, it is widely believed that a basic description of this phenomenon can be provided by a single-band Hubbard model or its derivative, the t-J model. The latter model is regarded as a minimal microscopic model, capable of describing the essential aspects of the complex physics of the cuprates. Unfortunately, in general case, neither of those two models can be solved exactly and therefore various approximate methods are used. Among them, the so-called mean-field methods provide a simple, yet fairly reasonable description of the cuprates. In particular, some of the main qualitative features of the phase diagram and the essential features of electronic spectrum are roughly reproduced. A standard mean-field approach to the t-J model, known under the name of renormalized mean-field theory (RMFT) goes beyond the Hartree-Fock approximation. Consequently, its fully consistent treatment requires a novel theoretical approach. This has been our original motivation to develop a general approach to the mean-field models, which is based on the maximum entropy (MaxEnt) principle. The method is presented in detail in Part II of this Thesis, and in Part III it is applied to study RMFT of the t-J model. First, we compare the results obtained within our formalism with those of the frequently used non-variational approach based entirely on the self-consistent equations. Also, various versions of RMFT are compared, and the most satisfactory of them is selected. This optimal version is subsequently used to study different versions of the original t-J Hamiltonian. As a result, upper critical concentration and doping dependence of the selected physical quantities (e.g. the superconducting gap and the Fermi velocity) is determined at low temperatures and in the absence of external magnetic field. We compare our findings both with theoretical results obtained from the Variational Monte Carlo (VMC) methods, as well as with the experimental data for selected cuprates. We show that the version of RMFT approach formulated in this Thesis provides a reasonable qualitative and in some cases semiquantitative rationalization of the principal characteristics of the hole-doped high-temperature superconductors at the optimal doping and in the overdoped regime. Possible extensions of the proposed analysis are mentioned at the end.