Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Modern Physics B

BINDING OF HOLES WITHIN THE EFFECTIVE SINGLE-BAND HAMILTONIAN FOR CuO 2 LAYERS

J. Bonča, Peter Prelovšek, Igor Sega

Published Oct 1, 1988• 3 citations
Publisher

Abstract

We have performed an exact numerical diagonalization of the effective single-band Hamiltonian for CuO 2 layers on a square lattice with 16 cells. Our results for one and two holes indicate in a range of exchange energies J/t on a possibility of pairing between holes, showing up in the binding energy and in the hole density correlations.
DOI
10.1142/s0217979288000779

Related papers

Exact-diagonalization study of the effective model for holes in the planar antiferromagnet

J. Bonča, Peter Prelovšek, Igor Sega

The effective single-band Hamiltonian for holes in the two-dimensional quantum antiferromagnet, relevant for the ${\mathrm{CuO}}_{2}$ layers in copper-oxide superconductors, is studied by the exact diagonalization of a finite-size system with 16 cells. Single- and two-hole ground-state properties are calculated. Pair-binding-energy and hole-density correlation functions indicate that two holes bind for moderate exchange interactions, even in the case of the extreme anisotropic-Ising limit.

Physical review. B, Condensed matter•Apr 1, 1989•197 citations

Exact-diagonalization study of electron-lattice coupling in the effective two-band t − J model

Yury Petrov, T. Egami

The effective two-band $t\ensuremath{-}J$ Hamiltonian for holes in Cu-O planes of cuprates is obtained from the three-band Hubbard Hamiltonian. In this model a doped oxygen hole together with two neighboring copper holes is treated as a composite spin-$\frac{1}{2}$ three-sites particle. The model is studied by exact diagonalization in a ${\mathrm{Cu}}_{16}{\mathrm{O}}_{32}$ square cluster. Both binding energy and hole-hole correlation function indicate that two holes bind together for $J/t>0.11$ and are predominantly located on the next-nearest oxygen sites in the same Cu-O chain. Electron-phonon interaction is studied in the adiabatic phonons approximation. Copper (\ensuremath{\pi},0) ``half-breathing'' mode is shown to couple strongly to doped holes and increase the hole-hole correlation as well as the binding energy. These results are compared with experimental data.

Physical review. B, Condensed matter•Oct 1, 1998•25 citations

HOLE BINDING IN AN EXTENDED MULTI-BAND HUBBARD MODEL

W. Stephan, Wolfgang von der Linden, Peter Horsch

An extended multi-band Hubbard model for the 2D CuO2 planes of high Tc superconductors is examined by exact diagonalization of the Hamiltonian for small clusters with periodic boundary conditions. Holes are shown to bind in the limit of strong onsite (Cu) and nearest neighbor (Cu-O) Coulomb repulsion. A simple explanation of the source of the binding energy is given in this strong-coupling limit.

International Journal of Modern Physics B•Oct 1, 1988•5 citations

High-Doping Regime in a Planar Model for Strongly Correlated Electrons

J. Bonča, Peter Prelovšek, Igor Sega

The exact diagonalization study of the effective single-band ( t - J ) model for strongly correlated electrons in a layered system of 16 cells, has been extended to a larger number of holes, i.e. up to N h = 4. A higher concentration of holes definitely reduces the range of antiferromagnetic correlations and the correlated state behaves more as a dilute system of correlated fermions. Still the hole-density correlations and moreover the four-point density correlations reveal a tendency to pairing in the intermediate regime of exchange couplings J / t , in contrast to the formation of droplets at larger J / t .

Europhysics Letters (EPL)•Sep 1, 1989•26 citations

One hole in a three-band model of a high-temperature superconductor

Iain B. Styles, M W Long

We study a three-band effective model of a CuO 2 plane for the simple case of a single hole, with the aim of investigating the nature of the ground state stabilized by the motion of a single hole on the CuO 2 lattice. Our model is derived from, and retains the essential physics of the Anderson lattice model, but is more amenable to further investigation by virtue of the lifting of the spin degeneracy on the copper sites provided by perturbation theory. We use the Lanczos algorithm to numerically solve a series of finite systems which tend to the CuO 2 plane in the thermodynamic limit. Although we only study finite systems, the largest systems are sufficiently large to demonstrate behaviour that is independent of the boundary conditions, and is hence representative of the behaviour in the thermodynamic limit. In order to gain a good understanding of the competing energy scales, we consider only a single hole at T = 0. Our calculations predict that the ground state of the three-band model for a single hole is strongly quantum, dominated by short-range dimer correlations, reminiscent of a resonating valence bond state. There is no evidence for a discontinuity in the occupation number, indicating that the system is not a Fermi liquid. These predictions are in contrast to those of the t – J model, where the hole motion alone predicts Nagaoka ferromagnetism for the planar system, and one must include magnetic exchange terms in order to obtain the experimentally observed low-spin ground state.

Journal of Physics A Mathematical and General•Aug 20, 2003•3 citations

Comparison of different ladder models

Eric Jeckelmann, Douglas J. Scalapino, Steven R. White

Using density matrix renormalization group calculations, we compare results obtained for the $t\ensuremath{-}J,$ one-band Hubbard, and three-band Hubbard models of a two-leg CuO ladder. Spin and charge gaps, pair binding energies, and effective pair hoppings are calculated for a wide range of parameters. All three models have an insulating state at a filling corresponding to one hole per Cu site. For physically relevant parameters their spin gaps are similar in size but they exhibit quite different charge gaps. We find that the binding energy of a pair of doped holes is of the order of the undoped ladder spin gap for all three models. The main difference between the models is the size of the effective pair hopping, which is significantly larger in the three-band model with parameters appropriate for CuO materials than in the other two models.

arXiv:cond-mat/9805116•Physical review. B, Condensed matter•Oct 1, 1998•52 citations
The effective single-band Hamiltonian for holes in the two-dimensional quantum antiferromagnet, relevant for the CuO2{\mathrm{CuO}}_{2}CuO2​ layers in copper-oxide superconductors, is studied by the exact diagonalization of a finite-size system with 16 cells. Single- and two-hole ground-state properties are calculated. Pair-binding-energy and hole-density correlation functions indicate that two holes bind for moderate exchange interactions, even in the case of the extreme anisotropic-Ising limit.
The effective two-band $t\ensuremath{-}J$ Hamiltonian for holes in Cu-O planes of cuprates is obtained from the three-band Hubbard Hamiltonian. In this model a doped oxygen hole together with two neighboring copper holes is treated as a composite spin-12\frac{1}{2}21​ three-sites particle. The model is studied by exact diagonalization in a Cu16O32{\mathrm{Cu}}_{16}{\mathrm{O}}_{32}Cu16​O32​ square cluster. Both binding energy and hole-hole correlation function indicate that two holes bind together for J/t>0.11J/t>0.11J/t>0.11 and are predominantly located on the next-nearest oxygen sites in the same Cu-O chain. Electron-phonon interaction is studied in the adiabatic phonons approximation. Copper (\ensuremath{\pi},0) ``half-breathing'' mode is shown to couple strongly to doped holes and increase the hole-hole correlation as well as the binding energy. These results are compared with experimental data.
The exact diagonalization study of the effective single-band ( t - J ) model for strongly correlated electrons in a layered system of 16 cells, has been extended to a larger number of holes, i.e. up to N h = 4. A higher concentration of holes definitely reduces the range of antiferromagnetic correlations and the correlated state behaves more as a dilute system of correlated fermions. Still the hole-density correlations and moreover the four-point density correlations reveal a tendency to pairing in the intermediate regime of exchange couplings J / t , in contrast to the formation of droplets at larger J / t .
We study a three-band effective model of a CuO 2 plane for the simple case of a single hole, with the aim of investigating the nature of the ground state stabilized by the motion of a single hole on the CuO 2 lattice. Our model is derived from, and retains the essential physics of the Anderson lattice model, but is more amenable to further investigation by virtue of the lifting of the spin degeneracy on the copper sites provided by perturbation theory. We use the Lanczos algorithm to numerically solve a series of finite systems which tend to the CuO 2 plane in the thermodynamic limit. Although we only study finite systems, the largest systems are sufficiently large to demonstrate behaviour that is independent of the boundary conditions, and is hence representative of the behaviour in the thermodynamic limit. In order to gain a good understanding of the competing energy scales, we consider only a single hole at T = 0. Our calculations predict that the ground state of the three-band model for a single hole is strongly quantum, dominated by short-range dimer correlations, reminiscent of a resonating valence bond state. There is no evidence for a discontinuity in the occupation number, indicating that the system is not a Fermi liquid. These predictions are in contrast to those of the t – J model, where the hole motion alone predicts Nagaoka ferromagnetism for the planar system, and one must include magnetic exchange terms in order to obtain the experimentally observed low-spin ground state.
Using density matrix renormalization group calculations, we compare results obtained for the $t\ensuremath{-}J,$ one-band Hubbard, and three-band Hubbard models of a two-leg CuO ladder. Spin and charge gaps, pair binding energies, and effective pair hoppings are calculated for a wide range of parameters. All three models have an insulating state at a filling corresponding to one hole per Cu site. For physically relevant parameters their spin gaps are similar in size but they exhibit quite different charge gaps. We find that the binding energy of a pair of doped holes is of the order of the undoped ladder spin gap for all three models. The main difference between the models is the size of the effective pair hopping, which is significantly larger in the three-band model with parameters appropriate for CuO materials than in the other two models.