We examine effective interactions of the 1D d-p model mapped to a typical one-dimensional(1D) model such as the Hubbard model or the t-J model by the numerical diagonalization method combined with the Luttinger liquid theory. Analysis of the effective coupling constants of the mapped model gives the relationship between these models without ambiguity. We find that the renormalized interaction is relatively weak, though the repulsion of the d-p model at Cu-sites is very strong. We also find that the d-p model corresponds to not the t-J model but the Hubbard model for wide range of the parameters. It suggests that the Hubbard model is more favorable than the t-J model as a effective model of the d-p model in the low energy limit.
We examine effective interactions of the 1D d-p model mapped to a typical one-dimensional(1D) model such as the Hubbard model or the t-J model by the numerical diagonalization method combined with the Luttinger liquid theory. Analysis of the effective coupling constants of the mapped model gives the relationship between these models without ambiguity. We find that the renormalized interaction is relatively weak, though the repulsion of the d-p model at Cu-sites is very strong. We also find that the d-p model corresponds to not the t-J model but the Hubbard model for wide range of the parameters. It suggests that the Hubbard model is more favorable than the t-J model as a effective model of the d-p model in the low energy limit.
We investigate the one-dimensional (1D) d-p model, simulating a Cu-O linear chain with strong Coulomb repulsion, by using the numerical diagonalization method. Using the Luttinger liquid theory, we obtained phase diagrams of the ground state on Ud-Upd plane, where Ud and Upd represent on-site interaction at d sites and the nearest-neighbor interaction between p and d sites, respectively. In the weak-coupling region, they agree with the g-ology; a superconducting phase [SC(I)] is restricted to attractive interaction ${\mathit{U}}_{\mathit{p}\mathit{d}}$0. On the other hand, in the strong-coupling region, we found a superconducting phase [SC(II)] for repulsive interaction Upd>\ensuremath{\Vert}Ud\ensuremath{\Vert} and an insulating state with a charge gap for Ud>Udc and Upd>Updc with critical values Udc and Updc at half-filling. Away from half-filling, another superconducting phase [SC(III)] appears for Ud\ensuremath{\gg}Upd>0; which has been found for Ud\ensuremath{\rightarrow}\ensuremath{\infty} in the previous paper [Physica C 205, 170 (1993)]. An analysis of the spin gap suggests that the SC(I) and SC(II) include the Luther-Emery region (with spin gap) in part, while the SC(III) belongs to the Tomonaga-Luttinger region (without spin gap) in whole.
We investigate the one-dimensional d - p model with the transfer energy t p p between the nearest neighbor p sites by the numerical diagonalization method. By calculating the critical exponent K ρ based on the Luttinger liquid relations and the paring correlation functions, we analyze the superconducting state induced by the effect of the large repulsion U d at the Cu site in cooperation with the transfer energy t p p . We obtain a phase diagram of the superconducting region on the filling n vs. U d parameter plane. It shows that the superconducting region appears when U d is larger than a certain critical value which decreases with increasing n . The results of paring correlation functions suggest that a singlet paring between the nearest neighbor p sites is most relevant to the superconductivity. We also discuss a relationship between the d - p model and the t - J model through an analysis of the dependence of K ρ on the parameters.
Using the numerical diagonalization method, we investigate the one-dimensional d-p model, simulating a Cu-O linear chain with strong Coulomb repulsions. Paying attention to the effect of the transfer energy tpp between the nearest neighbor oxygen-sites, we calculate the critical exponent of correlation functions Kρ based on the Luttinger liquid relations and the ground state energy E0(ϕ) as a function of an external flux ϕ. We find that the transfer tpp increases the charge susceptibility and the exponent Kρ in cooperation with the repulsion Ud at Cu-site. We also show that anomalous flux quantization occurs for Kρ>1. The superconducting region is presented on a phase diagram of Ud vs. tpp plane.
We review the progress in the theory of one-dimensional (ID) Fermi liquids which has occurred over the past decade. The usual Fermi liquid theory, based on a quasi-particle picture, breaks down in one dimension because of the Peierls divergence in the particle-hole bubble, producing anomalous dimensions of operators, and because of charge-spin separation. Both are related to the importance of scattering processes transferring finite momentum. A description of the low-energy properties of gapless 1D quantum systems can be based on the exactly solvable Luttinger model which incorporates these features, and whose correlation functions can be calculated. Special properties of the eigenvalue spectrum, parameterized by one renormalized velocity and one effective coupling constant per degree of freedom, fully describe the physics of this model. Other gapless 1D models share these properties in a low-energy subspace. The concept of a "Luttinger liquid" implies that their low-energy properties are described by an effective Luttinger model, and constitutes the universality class of these quantum systems. Once the mapping on the Luttinger model is achieved, one has an asymptotically exact solution of the 1D many-body problem. Lattice models identified as Luttinger liquids include the 1D Hubbard model off half-filling, and variants such as the t-J- or the extended Hubbard model. In addition, 1D electron-phonon systems or metals with impurities can be Luttinger liquids, as well as the edge states in the quantum Hall effect.
We investigated the one-dimensional extended Hubbard model with the on-site interaction U and the nearest-neighbor interaction V by using the numerical diagonalization method. Assuming the Luttinger liquid relations, we obtained the phase diagram of the ground state on the U - V plane. In the weak coupling region, the phase diagram agrees with the result of g -ology. On the other hand, in the strong coupling region for V ≫∣ t ∣, a novel superconducting phase appears both for positive and negative U . We also investigated the charge gap and the spin gap. The results suggest that the superconducting phase extends over the Tomonaga-Luttinger region (without spin gap) and the Luther-Emery region (with spin gap).
We study a model of a quantum Hall system with the electrons confined to a narrow, linear channel. The system is mapped to a one-dimensional (1D) system which in the low-energy approximation has the form of a Luttinger liquid with different interactions between particles of equal and of opposite chiralities. In a previous paper (Part I) [M. Horsdal and J. M. Leinaas, Phys. Rev. B 76, 195321 (2007)], we studied this mapping at the microscopic level, and examined how the interaction in the two-dimensional (2D) system renormalizes 1D Luttinger liquid parameters. We follow up this study here and derive the low-energy form of the 2D electron correlation function by applying the mapping from the 1D correlation function. The derived expression has a natural separation in a bulk part, which is not modified by interactions, and an edge part, which is modified. We study the effect of interactions on the electron density and on the asymptotic form of the correlation function. The asymptotic parameter is found to be consistent with the expected value from the Luttinger liquid theory, but deviations from the asymptotic form are found in a rather wide intermediate interval. We suggest some questions of interest for further study.