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The Hubbard model beyond the two-pole approximation: a composite operator method study

Adolfo Avella

arXiv:1401.8110The European Physical Journal BFeb 1, 201419 citations

Perturbational approach to the one particle properties of the Hubbard model

Thomas Pruschke

The European Physical Journal BOct 1, 199015 citations

Single-particle spectral density of the Hubbard model

B. Mehlig, Henk J. Eskes, R. Hayn +1 more

We calculate the single-particle spectral function for the Hubbard model within the framework of a projection technique equivalent to the two-pole approximation. We show that the two-pole approximation can be well understood as an average characterization of the upper and the lower Hubbard bands, rather than describing a dispersive quasiparticle. By comparing with numerical spectra of finite Hubbard rings and of a 4\ifmmode\times\else\texttimes\fi{}4 cluster [P. W. Leung et al., Phys. Rev. B 46, 11 779 (1992)], we show that the present approximation is capable of reproducing essential properties of the single-particle spectral function. In particular, the two-pole spectrum is characterized by a direct gap, in agreement with the exact spectrum. We emphasize the role of local antiferromagnetic correlations.We calculate the single-particle spectral function for the Hubbard model within the framework of a projection technique equivalent to the two-pole approximation. We show that the two-pole approximation can be well understood as an average characterization of the upper and the lower Hubbard bands, rather than describing a dispersive quasiparticle. By comparing with numerical spectra of finite Hubbard rings and of a 4\ifmmode\times\else\texttimes\fi{}4 cluster [P. W. Leung et al., Phys. Rev. B 46, 11 779 (1992)], we show that the present approximation is capable of reproducing essential properties of the single-particle spectral function. In particular, the two-pole spectrum is characterized by a direct gap, in agreement with the exact spectrum. We emphasize the role of local antiferromagnetic correlations.

Physical review. B, Condensed matterJul 15, 199534 citations

Fermi surface evolution of the 2D Hubbard model within a novel four-pole approximation

Andrea Di Ciolo, Adolfo Avella

We present a novel solution of the 2D Hubbard model in the framework of the Composite Operator Method within a four-pole approximation. We adopt a basis of four fields: the two Hubbard operators plus two fields describing the Hubbard transitions dressed by nearest-neighbor spin fluctuations. We include these nonlocal operators because spin fluctuations play a dominant role in strongly correlated electronic systems with respect to other types of nonlocal charge, pair and double-occupancy fluctuations. The approximate solution performs very well once compared with advanced (semi-) numerical methods from the weak-to the strong-coupling regime, being by far less computational-resource demanding. We adopt this solution to study the single-particle properties of the model in the strong coupling regime, where the effects of strong short-range magnetic correlations are more relevant and could be responsible for anomalous features. In particular, we will focus on the characterization of the Fermi surface and of its evolution with doping.We present a novel solution of the 2D Hubbard model in the framework of the Composite Operator Method within a four-pole approximation. We adopt a basis of four fields: the two Hubbard operators plus two fields describing the Hubbard transitions dressed by nearest-neighbor spin fluctuations. We include these nonlocal operators because spin fluctuations play a dominant role in strongly correlated electronic systems with respect to other types of nonlocal charge, pair and double-occupancy fluctuations. The approximate solution performs very well once compared with advanced (semi-) numerical methods from the weak-to the strong-coupling regime, being by far less computational-resource demanding. We adopt this solution to study the single-particle properties of the model in the strong coupling regime, where the effects of strong short-range magnetic correlations are more relevant and could be responsible for anomalous features. In particular, we will focus on the characterization of the Fermi surface and of its evolution with doping.

AIP AdvancesOct 1, 20180 citations

4-pole analysis of the two-dimensional Hubbard model

Satoru Odashima, Adolfo Avella, Ferdinando Mancini

arXiv:cond-mat/0412085Physica B Condensed MatterFeb 18, 20052 citations

LOW DENSITY HUBBARD MODEL IN TWO AND THREE DIMENSIONS

Sergei Khlebnikov

We consider two- and three-dimensional repulsive Hubbard models at low density, using the gas approximation. The large-U three-dimensional model is shown to behave as a Fermi liquid and the corresponding two-particle scattering length is found. In the two-dimensional case we find that the gas approximation is inconsistent, as indicated by an isolated pole of the two-particle Green function below the occupied states in the upper half-plane. This behaviour is specific to the lattice system as opposed to the continuum two-dimensional Fermi gas with short-range repulsion.We consider two- and three-dimensional repulsive Hubbard models at low density, using the gas approximation. The large-U three-dimensional model is shown to behave as a Fermi liquid and the corresponding two-particle scattering length is found. In the two-dimensional case we find that the gas approximation is inconsistent, as indicated by an isolated pole of the two-particle Green function below the occupied states in the upper half-plane. This behaviour is specific to the lattice system as opposed to the continuum two-dimensional Fermi gas with short-range repulsion.

Modern Physics Letters BMay 20, 19920 citations

Single-particle properties of the Hubbard model in a novel three-pole approximation

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