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Physical review. B, Condensed matter

Collective-mode approximations in the two-dimensional large- N t−J model

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

Published Jun 15, 1999• 0 citations
Publisher

Abstract

The one-electron spectral function $\ensuremath{\rho}(\mathit{k},\ensuremath{\omega})$ for the large-$\mathcal{N}$ $t\ensuremath{-}J$ model typically consists of two distinct peaks: a dispersive quasiparticle and a lower-energy incoherent structure. This is reminiscent of the spectral function of the weak coupling Hubbard model in which the electron is coupled to antiferromagnetic spin fluctuations. In both theories, the two-peaked pattern can be traced to the frequency dependence of the (normal) electron self-energy $\ensuremath{\Sigma}(\mathit{k},\ensuremath{\omega})$. What interaction causes this particular $\ensuremath{\omega}$ dependence of $\ensuremath{\Sigma}$? In the weak coupling case it is clearly the emission and absorption of an antiferromagnetic spin fluctuation by the electron. In the slave boson formulation of the large-$\mathcal{N}$ $t\ensuremath{-}J$ model, there are six bosonic excitations: the slave bosons, the constraint field, and the real and imaginary parts of the hopping amplitudes in both the x and y directions. None of these are obviously related to a spin fluctuation propagator. These bosons have the unusual property of transmuting in flight---that is, they are not eigenstates. In order to try to make physical sense of the interaction that is primarily responsible for the frequency dependence of $\ensuremath{\Sigma}$ and the structure of $\ensuremath{\rho}(\mathit{k},\ensuremath{\omega})$, we investigate the transformation to a representation in which the boson propagator matrix is diagonal and extract the contributions of the slave bosons and the constraint field, which appear to be of particular importance.

DOI
10.1103/physrevb.59.14969

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The one-electron spectral function \ensuremathρ(k,\ensuremathω)\ensuremath{\rho}(\mathit{k},\ensuremath{\omega})\ensuremathρ(k,\ensuremathω) for the large-N\mathcal{N}N t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model typically consists of two distinct peaks: a dispersive quasiparticle and a lower-energy incoherent structure. This is reminiscent of the spectral function of the weak coupling Hubbard model in which the electron is coupled to antiferromagnetic spin fluctuations. In both theories, the two-peaked pattern can be traced to the frequency dependence of the (normal) electron self-energy \ensuremathΣ(k,\ensuremathω)\ensuremath{\Sigma}(\mathit{k},\ensuremath{\omega})\ensuremathΣ(k,\ensuremathω). What interaction causes this particular \ensuremathω\ensuremath{\omega}\ensuremathω dependence of \ensuremathΣ\ensuremath{\Sigma}\ensuremathΣ? In the weak coupling case it is clearly the emission and absorption of an antiferromagnetic spin fluctuation by the electron. In the slave boson formulation of the large-N\mathcal{N}N t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model, there are six bosonic excitations: the slave bosons, the constraint field, and the real and imaginary parts of the hopping amplitudes in both the x and y directions. None of these are obviously related to a spin fluctuation propagator. These bosons have the unusual property of transmuting in flight---that is, they are not eigenstates. In order to try to make physical sense of the interaction that is primarily responsible for the frequency dependence of \ensuremathΣ\ensuremath{\Sigma}\ensuremathΣ and the structure of \ensuremathρ(k,\ensuremathω)\ensuremath{\rho}(\mathit{k},\ensuremath{\omega})\ensuremathρ(k,\ensuremathω), we investigate the transformation to a representation in which the boson propagator matrix is diagonal and extract the contributions of the slave bosons and the constraint field, which appear to be of particular importance.
Calculations of the one-electron spectral function of the $t\ensuremath{-}J$ model on a two-dimensional square lattice are described. A large-N\mathcal{N}N generalization of the $t\ensuremath{-}J$ model is used to develop 1/N1/\mathcal{N}1/N expansions, and the $t\ensuremath{-}J$ model constraint is enforced by slave bosons. The saddle point about which the 1/N1/\mathcal{N}1/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/N1/\mathcal{N}1/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/tJ/tJ/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.
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