The so-called three-band Hubbard model is generally believed to be a good model for fermions on a CuO 2 lattice and to contain key features allowing to understand high-temperature superconductivity in the cuprates. A simpler and more popular model is the one-band Hubbard model. In this thesis,an extended one-band Hubbard model is derived from the three-band model. First, some mathematical background is given, as well as an introduction to Hubbard-like models. Then, to derive the extended one-band Hubbard model, the CuO 2 lattice is divided into clusters of one Cu and two O sites, and a variant of the Feshbach method is used to replace each such cluster by a single lattice site. To nd a suitable one-band model, all Hamiltonian matrix elements are matched between the two models. Finally, dierent sets of three-band parameters are considered, and it is studied how this aects the parameters in the extended one-band Hubbard model.The so-called three-band Hubbard model is generally believed to be a good model for fermions on a CuO 2 lattice and to contain key features allowing to understand high-temperature superconductivity in the cuprates. A simpler and more popular model is the one-band Hubbard model. In this thesis,an extended one-band Hubbard model is derived from the three-band model. First, some mathematical background is given, as well as an introduction to Hubbard-like models. Then, to derive the extended one-band Hubbard model, the CuO 2 lattice is divided into clusters of one Cu and two O sites, and a variant of the Feshbach method is used to replace each such cluster by a single lattice site. To nd a suitable one-band model, all Hamiltonian matrix elements are matched between the two models. Finally, dierent sets of three-band parameters are considered, and it is studied how this aects the parameters in the extended one-band Hubbard model.

Jan 1, 20111 citation

Pairing in the two-dimensional Hubbard model: An exact diagonalization study

H. Q. Lin, J. E. Hirsch, Douglas J. Scalapino

We have studied the pair susceptibilities for all possible pair wave functions that fit on a two-dimensional (2D) eight-site Hubbard cluster by exact diagonalization of the Hamiltonian. Band fillings corresponding to four and six electrons were studied (two or four holes in the half-filled band) for a wide range of Hubbard interaction strengths and temperatures. Our results show that all pairing susceptibilities are suppressed by the Hubbard repulsion. We have also carried out perturbation-theory calculations which show that the leading-order ${U}^{2}$ contributions to the d-wave pair susceptibility suppresses d-wave pairing over a significant temperature range. These results are consistent with recent Monte Carlo results and provide further evidence suggesting that the 2D Hubbard model does not exhibit superconductivity.We have studied the pair susceptibilities for all possible pair wave functions that fit on a two-dimensional (2D) eight-site Hubbard cluster by exact diagonalization of the Hamiltonian. Band fillings corresponding to four and six electrons were studied (two or four holes in the half-filled band) for a wide range of Hubbard interaction strengths and temperatures. Our results show that all pairing susceptibilities are suppressed by the Hubbard repulsion. We have also carried out perturbation-theory calculations which show that the leading-order ${U}^{2}$ contributions to the d-wave pair susceptibility suppresses d-wave pairing over a significant temperature range. These results are consistent with recent Monte Carlo results and provide further evidence suggesting that the 2D Hubbard model does not exhibit superconductivity.

Physical review. B, Condensed matterMay 1, 198880 citations

Small-cluster calculations for the simple and extended Hubbard models

J. Callaway, D. P. Chen, D. G. Kanhere +1 more

The single-band Hubbard model (both with and without first-neighbor interactions) is studied by exact diagonalization on several one- and two-dimensional clusters, ranging from four to nine sites, including rings and arrangements of squares. Occupancies include the half-filled band (one electron per site) and configurations with one and two holes in the half-filled band. Ground-state properties are determined for a wide range of parameters. We discuss the phase diagram in the (U,V) plane and consider spin, charge, and pairing correlations. The binding of a pair of holes is investigated. Circumstances in which binding and pairing are enhanced by first-neighbor interactions are described.The single-band Hubbard model (both with and without first-neighbor interactions) is studied by exact diagonalization on several one- and two-dimensional clusters, ranging from four to nine sites, including rings and arrangements of squares. Occupancies include the half-filled band (one electron per site) and configurations with one and two holes in the half-filled band. Ground-state properties are determined for a wide range of parameters. We discuss the phase diagram in the (U,V) plane and consider spin, charge, and pairing correlations. The binding of a pair of holes is investigated. Circumstances in which binding and pairing are enhanced by first-neighbor interactions are described.

Physical review. B, Condensed matterJul 1, 199041 citations

Electronic structure of the Hubbard and extended Hubbard models: An exact diagonalization study

Y. Ohta, Kenji Tsutsui, Wataru Koshibae +1 more

Physica B Condensed MatterFeb 1, 19941 citation

{U}^{2}

contributions to the d-wave pair susceptibility suppresses d-wave pairing over a significant temperature range. These results are consistent with recent Monte Carlo results and provide further evidence suggesting that the 2D Hubbard model does not exhibit superconductivity.