Proceedings of the Estonian Academy of Sciences Physics Mathematics

TEMPERATURE DEPENDENCE OF THE ENERGY SPECTRUMOFTHE TWO-DIMENSIONAL t-J MODEL

O Shvaikovsky, A. Sherman

Published Jan 1, 1994• 0 citations

Abstract

A motion of a hole in a two-dimensional antiferromagnet is considered in the framework of the #-J model.A temperature dependence of the lowest energy band is calculated for the range T/t £ 0.1 where T and ¢ are the temperature and the hopping constant, respectively.For the exchange constant J= J. =~0 .52 f the lowest energy is shown to be degenerate along the boundaries of the magnetic Brillouin zone.For J < J, the lowest energy is achieved in the points q = (£n/2,+n/2) while for larger J, @ е points (+n,o), (0,%n) of the Brillouin zone.The critical value is independent on 7. А perceptible dependence of the quasiparticle energy on Tis observed for Т »203 J

DOI: 10.3176/phys.math.1994.3.06

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Proceedings of the Estonian Academy of Sciences Physics Mathematics

TEMPERATURE DEPENDENCE OF THE ENERGY SPECTRUMOFTHE TWO-DIMENSIONAL t-J MODEL

O Shvaikovsky, A. Sherman

Published Jan 1, 1994• 0 citations

Publisher

Abstract

DOI: 10.3176/phys.math.1994.3.06

Related papers

One-hole motion in the anisotropic three-dimensional antiferromagnet

Weijie Zhang, Jue-lian Shen

We have investigated one-hole motion in the anisotropic three-dimensional (A3D) quantum antiferromagnet by use of the A3D t-J model in a simple cubic lattice. The hopping matrix element and the Heisenberg exchange energy are t and J in the xy plane. They are ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ and ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$ in the z direction. Within the self-consistent mean-field approximation, the hole spectral function has been calculated by use of an iterative technique. We find that the quasiparticle picture still holds and the lowest-energy quasiparticle state has momentum either k=(\ensuremath{\pi}/2,\ensuremath{\pi}/2,\ensuremath{\pi}/2) or k=(\ensuremath{\pi}/2,\ensuremath{\pi}/2,0) depending on the parameters of the model. Holding J and ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$ constant and allowing ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ to increase, the spectral weight and the peak height of the quasiparticle decreases. In the quasi-two-dimensional cases with small ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ and ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$, the spectral weight and the peak height of the quasiparticle are smaller than those in the exact two-dimensional case.We have investigated one-hole motion in the anisotropic three-dimensional (A3D) quantum antiferromagnet by use of the A3D t-J model in a simple cubic lattice. The hopping matrix element and the Heisenberg exchange energy are t and J in the xy plane. They are ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ and ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$ in the z direction. Within the self-consistent mean-field approximation, the hole spectral function has been calculated by use of an iterative technique. We find that the quasiparticle picture still holds and the lowest-energy quasiparticle state has momentum either k=(\ensuremath{\pi}/2,\ensuremath{\pi}/2,\ensuremath{\pi}/2) or k=(\ensuremath{\pi}/2,\ensuremath{\pi}/2,0) depending on the parameters of the model. Holding J and ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$ constant and allowing ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ to increase, the spectral weight and the peak height of the quasiparticle decreases. In the quasi-two-dimensional cases with small ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ and ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$, the spectral weight and the peak height of the quasiparticle are smaller than those in the exact two-dimensional case.

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Spectral function of the two-dimensional large-Nt-Jmodel

Marilyn F. Bishop, Zane P. Gibbs, T. McMullen

Calculations of the one-electron spectral function of the $t\ensuremath{-}J$ model on a two-dimensional square lattice are described. A large- $\mathcal{N}$ generalization of the $t\ensuremath{-}J$ model is used to develop $1/\mathcal{N}$ expansions, and the $t\ensuremath{-}J$ model constraint is enforced by slave bosons. The saddle point about which the $1/\mathcal{N}$ expansion is carried out is chosen to be uniform in both space and time, and self-energies are calculated to next-to-leading order in $1/\mathcal{N}$ as in the work of Z. Wang et al. [Phys. Rev. Lett. 67, 2733 (1991)]. The results of computations of the one-electron electron spectral functions for wave vectors throughout the Brillouin zone are presented for several values of the exchange coupling $J/t$ and doping $\ensuremath{\delta}$. A sharp dispersive quasiparticle peak is found near the Fermi energy. Additional spectral weight occurs at lower frequencies, and this arises from features in the normal self-energy. These features are qualitatively similar to the self-energy obtained by Kampf and Schrieffer [Phys. Rev. B 41, 6399 (1990)] from a parametrized model of an electron coupled to antiferromagnetic spin fluctuations that leads to shadow band structure in the one-electron spectral function.Calculations of the one-electron spectral function of the $t\ensuremath{-}J$ model on a two-dimensional square lattice are described. A large-$\mathcal{N}$ generalization of the $t\ensuremath{-}J$ model is used to develop $1/\mathcal{N}$ expansions, and the $t\ensuremath{-}J$ model constraint is enforced by slave bosons. The saddle point about which the $1/\mathcal{N}$ expansion is carried out is chosen to be uniform in both space and time, and self-energies are calculated to next-to-leading order in $1/\mathcal{N}$ as in the work of Z. Wang et al. [Phys. Rev. Lett. 67, 2733 (1991)]. The results of computations of the one-electron electron spectral functions for wave vectors throughout the Brillouin zone are presented for several values of the exchange coupling $J/t$ and doping $\ensuremath{\delta}$. A sharp dispersive quasiparticle peak is found near the Fermi energy. Additional spectral weight occurs at lower frequencies, and this arises from features in the normal self-energy. These features are qualitatively similar to the self-energy obtained by Kampf and Schrieffer [Phys. Rev. B 41, 6399 (1990)] from a parametrized model of an electron coupled to antiferromagnetic spin fluctuations that leads to shadow band structure in the one-electron spectral function.

Physical review. B, Condensed matterJun 15, 19992 citations

{\mathit{S}}_{\mathit{z}}

, corresponding to ferromagnetically ordered regions of different size around the hole. For an infinite lattice, the shapes and relative positions of the lowest bands are computed by means of the Lanczos method. The formation process of the ferromagnetically ordered region in the one-hole ground state is discussed. It is connected with a characteristic dependence of the band energy on J/t for different

{\mathit{S}}_{\mathit{z}}

. The shapes of the magnon cloud around the hole and the point symmetries of the eigenfunctions are determined for various points in the Brillouin zone and for different bands of interest.

Calculations of the one-electron spectral function of the $t\ensuremath{-}J$ model on a two-dimensional square lattice are described. A large-

\mathcal{N}

generalization of the $t\ensuremath{-}J$ model is used to develop

1/\mathcal{N}

expansions, and the $t\ensuremath{-}J$ model constraint is enforced by slave bosons. The saddle point about which the

1/\mathcal{N}

expansion is carried out is chosen to be uniform in both space and time, and self-energies are calculated to next-to-leading order in

1/\mathcal{N}

as in the work of Z. Wang et al. [Phys. Rev. Lett. 67, 2733 (1991)]. The results of computations of the one-electron electron spectral functions for wave vectors throughout the Brillouin zone are presented for several values of the exchange coupling

J/t

and doping $\ensuremath{\delta}$. A sharp dispersive quasiparticle peak is found near the Fermi energy. Additional spectral weight occurs at lower frequencies, and this arises from features in the normal self-energy. These features are qualitatively similar to the self-energy obtained by Kampf and Schrieffer [Phys. Rev. B 41, 6399 (1990)] from a parametrized model of an electron coupled to antiferromagnetic spin fluctuations that leads to shadow band structure in the one-electron spectral function.