Physical review. B, Condensed matter

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

J. Bonča, Peter Prelovšek, Igor Sega

Published Apr 1, 1989• 197 citations

Abstract

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.

DOI: 10.1103/physrevb.39.7074

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

J. Bonča, Peter Prelovšek, Igor Sega

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.

International Journal of Modern Physics BOct 1, 19883 citations

Ground state of the strong-coupling Hubbard Hamiltonian: A numerical diagonalization study

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Physical review. B, Condensed matterJan 1, 198853 citations

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

Yury Petrov, T. Egami

Physical review. B, Condensed matterOct 1, 199825 citations

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

J. Bonča, Peter Prelovšek, Igor Sega

Europhysics Letters (EPL)Sep 1, 198926 citations

Cumulant-expansion study of holes in quantum antiferromagnets

P. Prelovek, Igor Sega, J. Bona

Physical review. B, Condensed matterDec 1, 199022 citations

Interaction of holes in a Hubbard antiferromagnet and high-temperature superconductivity

S. A. Trugman

Physical review. B, Condensed matterFeb 1, 1988502 citations

Physical review. B, Condensed matter

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

J. Bonča, Peter Prelovšek, Igor Sega

Published Apr 1, 1989• 197 citations

Publisher

Abstract

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.

DOI: 10.1103/physrevb.39.7074

Related papers

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

J. Bonča, Peter Prelovšek, Igor Sega

International Journal of Modern Physics BOct 1, 19883 citations

Ground state of the strong-coupling Hubbard Hamiltonian: A numerical diagonalization study

Efthimios Kaxiras, Efstratios Manousakis

We exactly diagonalize the effective Hamiltonian obtained from the Hubbard model in the strong-coupling limit for a two-dimensional $\sqrt{10}\ifmmode\times\else\texttimes\fi{}\sqrt{10}$ size square lattice. The effective Hamiltonian operates on a restricted Hilbert space containing only states with singly occupied sites, which makes the diagonalization possible within reasonable computational time for the above lattice. The ground-state energy and wave function are obtained for several values of the coupling ratio $\frac{t}{U}$ and the doping fraction $x$ . We find three different phases in the ( $x,\frac{t}{U}$ ) phase diagram. The first is characterized by antiferromagnetic order which extends to the longest possible distance in the 10-site system. The second and third phases are characterized by antiferromagnetic and ferromagnetic short-range correlations, respectively. We comment on the possible relevance of the results to the recently discovered high-temperature copper-oxide superconductors.We exactly diagonalize the effective Hamiltonian obtained from the Hubbard model in the strong-coupling limit for a two-dimensional $\sqrt{10}\ifmmode\times\else\texttimes\fi{}\sqrt{10}$ size square lattice. The effective Hamiltonian operates on a restricted Hilbert space containing only states with singly occupied sites, which makes the diagonalization possible within reasonable computational time for the above lattice. The ground-state energy and wave function are obtained for several values of the coupling ratio $\frac{t}{U}$ and the doping fraction $x$. We find three different phases in the ($x,\frac{t}{U}$) phase diagram. The first is characterized by antiferromagnetic order which extends to the longest possible distance in the 10-site system. The second and third phases are characterized by antiferromagnetic and ferromagnetic short-range correlations, respectively. We comment on the possible relevance of the results to the recently discovered high-temperature copper-oxide superconductors.

Physical review. B, Condensed matterJan 1, 198853 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.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 matterOct 1, 199825 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 .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, 198926 citations

Cumulant-expansion study of holes in quantum antiferromagnets

P. Prelovek, Igor Sega, J. Bona

The states of a single hole and of two holes in the planar quantum antiferromagnet are studied within the t-J model by performing the cumulant expansion in t/J and in the exchange anisotropy \ensuremath{\gamma}. Ground-state energies are calculated up to the n=12 order in t/J and to the m=6 order in \ensuremath{\gamma}. It is shown that results, which can be extended to smaller J/t, represent a very helpful supplement to exact diagonalization methods. In particular they yield finite-size corrections to previous results on the dispersion of single-hole states and to the binding energy of two holes, giving also more insight into the origin of binding.The states of a single hole and of two holes in the planar quantum antiferromagnet are studied within the t-J model by performing the cumulant expansion in t/J and in the exchange anisotropy \ensuremath{\gamma}. Ground-state energies are calculated up to the n=12 order in t/J and to the m=6 order in \ensuremath{\gamma}. It is shown that results, which can be extended to smaller J/t, represent a very helpful supplement to exact diagonalization methods. In particular they yield finite-size corrections to previous results on the dispersion of single-hole states and to the binding energy of two holes, giving also more insight into the origin of binding.

Physical review. B, Condensed matterDec 1, 199022 citations

Interaction of holes in a Hubbard antiferromagnet and high-temperature superconductivity

S. A. Trugman

The ${\mathrm{CuO}}_{2}$ planes in the high-temperature superconductors are described by a two-dimensional Hubbard model. The model is investigated for an infinite system with one and two electrons less than half filling. The method used is to diagonalize the Hamiltonian exactly within a retained portion of the Hilbert space. A single hole is found not to be localized by a string potential that increases linearly with distance, although it does have a large effective mass. A pair of holes, which naively should be quite mobile, is found instead to be extremely heavy due to a previously unappreciated frustration effect that impedes their motion. This lack of mobility increases the energy of the pair so that they do not bind, contrary to some recently published results using mean field theory or intuitive arguments. The energy of one- and two-hole states is calculated as a function of wavevector k. The comparative energy of different angular momentum channels and magnetic polaron effects are discussed.The ${\mathrm{CuO}}_{2}$ planes in the high-temperature superconductors are described by a two-dimensional Hubbard model. The model is investigated for an infinite system with one and two electrons less than half filling. The method used is to diagonalize the Hamiltonian exactly within a retained portion of the Hilbert space. A single hole is found not to be localized by a string potential that increases linearly with distance, although it does have a large effective mass. A pair of holes, which naively should be quite mobile, is found instead to be extremely heavy due to a previously unappreciated frustration effect that impedes their motion. This lack of mobility increases the energy of the pair so that they do not bind, contrary to some recently published results using mean field theory or intuitive arguments. The energy of one- and two-hole states is calculated as a function of wavevector k. The comparative energy of different angular momentum channels and magnetic polaron effects are discussed.

Physical review. B, Condensed matterFeb 1, 1988502 citations

The effective single-band Hamiltonian for holes in the two-dimensional quantum antiferromagnet, relevant for the

{\mathrm{CuO}}_{2}

\frac{t}{U}

and the doping fraction

x

. We find three different phases in the (

x,\frac{t}{U}

) phase diagram. The first is characterized by antiferromagnetic order which extends to the longest possible distance in the 10-site system. The second and third phases are characterized by antiferromagnetic and ferromagnetic short-range correlations, respectively. We comment on the possible relevance of the results to the recently discovered high-temperature copper-oxide superconductors.

\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.

The

{\mathrm{CuO}}_{2}

planes in the high-temperature superconductors are described by a two-dimensional Hubbard model. The model is investigated for an infinite system with one and two electrons less than half filling. The method used is to diagonalize the Hamiltonian exactly within a retained portion of the Hilbert space. A single hole is found not to be localized by a string potential that increases linearly with distance, although it does have a large effective mass. A pair of holes, which naively should be quite mobile, is found instead to be extremely heavy due to a previously unappreciated frustration effect that impedes their motion. This lack of mobility increases the energy of the pair so that they do not bind, contrary to some recently published results using mean field theory or intuitive arguments. The energy of one- and two-hole states is calculated as a function of wavevector k. The comparative energy of different angular momentum channels and magnetic polaron effects are discussed.