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Quasi-particle spectrum of the Hubbard model: Strong intra atomic interaction limit

Rishabh Kishore, A. R. Dossantos

Published Nov 1, 1978• 0 citations
OpenAlex

Abstract

We have exploited a self consistent many body theory to calculate the quasi-particle spectrum of the Hubbard model, in the limit of strong intraatomic interaction. The quasi-particle energy of each band of the spectrum, consisting of two bands, is calculated exactly up to terms linear in the hopping-integral.

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Philosophical Magazine B•May 1, 1999•1 citation
We study the quasiparticle spectrum of the Hubbard model by using a projection-operator formalism of the Green's function. In the weak-electron-correlation regime, we obtain the exact results up to second order in the intra-atomic interaction. For strong electron correlations, the quasiparticle spectrum consists of two bands. For each band, the quasiparticle energy is obtained exactly up to the first order in the transfer integral. We also propose a semiclassical approximation which gives the above-mentioned exact results in proper limits.
The single-particle Green's function for the strong-coupling limit of the single-band Hubbard model ( t-J model) at half-filling is calculated numerically using a Lanczos algorithm. Two-dimensional systems of up to 18 sites with periodic boundary conditions are examined, and evidence is presented for a coherent quasi-particle band of width J which emerges at the low-energy edge of the incoherent spectrum. We find the quasi-particle dispersion to be consistent with ε k = ( J /2)[cos ( k x ) + cos ( k y )] 2 , corresponding to effective next-nearest-neighbour hopping.
The self-consistent theory of the correlation effects in Highly Correlated Systems(HCS) is presented. The novel Irreducible Green's Functions(IGF) method is discused in detail for the Hubbard model and random Hubbard model. The interpolative solution for the quasiparticle spectrum, which is valid for both the atomic and band limit is obtained. The (IGF) method permits to calculate the quasiparticle spectra of many-particle systems with the complicated spectra and strong interaction in a very natural and compact way. The inelastic scattering corrections leads to the damping of the quasiparticles and are the main topic of the present consideration. The calculation of the damping has been done in a self-consistent way for both limits. For the random Hubbard model the weak coupling case has been considered and the self-energy operator has been calculated using the combination of the IGF method and Coherent Potential Approximation (CPA). The other applications of the method to s-f model, Anderson model, Heisenberg antiferromagnet, electron-phonon interaction models are discussed briefly.
The Hubbard hamiltonian is analysed by means of Gutzwiller's variational scheme for both the nondegenerate and the degenerate band models. The single-particle excitations in the correlated ground state, which is determined by a balance between the electron hopping energy and the intra-atomic interaction energy, are investigated for arbitrary electron density and arbitrary correlation strength. It is found that the single-particle excitation energies forming a quasi-energy band. The centre of gravity of the quasi band is shifted from that of the bare band, and the bulk part of the density of states function for the quasi particles is narrowed by the correlation effect. Both the shift and the narrowing are spin-dependent. In the limit of strong correlation, our results agree with those obtained by Harris and Lange (1967) and Roth (1969).
We present an analytic solution of the self consistent random phase approximation equations for the half-filled Hubbard model, in the strong coupling limit. In the half-filled limit the Hubbard model shows antiferromagnetic ordering. The self energy is calculated by considering processes whereby the electrons emit and absorb low frequency spin waves, which are the Goldstone modes of the broken symmetry phase. We examine the electronic spectrum, which is dominated by the broad incoherent portions of the spectrum associated with the upper and lower Hubbard bands. The quasi-particle spectrum has a divergent wave function renormalization, indicating a divergent renormalization of the quasi-particle mass and zero quasi-particle weight, as in a non-Fermi liquid. The self consistency equation determined from the Goldstone modes in the susceptibility shows that the antiferromagnetism is prohibited in one and two dimensions but not in three. The magnetic ordering temperature is determined by dimensionality and the magnitude of the Anderson kinetic exchange of the effective Heisenberg Hamiltonian.