Van Hove singularities in the paramagnetic phase of the Hubbard model: DMFT study

Rok Žitko, Janez Bonča, and Thomas Pruschke
Phys. Rev. B 80, 245112 – Published 16 December 2009

Abstract

Using the dynamical mean-field theory (DMFT) with the numerical renormalization-group impurity solver we study the paramagnetic phase of the Hubbard model with the density of states (DOS) corresponding to the three-dimensional (3D) cubic lattice and the two-dimensional (2D) square lattice, as well as a DOS with inverse square-root singularity. We show that the electron correlations rapidly smooth out the square-root van Hove singularities (kinks) in the spectral function for the 3D lattice and that the Mott metal-insulator transition (MIT) as well as the magnetic-field-induced MIT differ only little from the well-known results for the Bethe lattice. The consequences of the logarithmic singularity in the DOS for the 2D lattice are more dramatic. At half filling, the divergence pinned at the Fermi level is not washed out, only its integrated weight decreases as the interaction is increased. While the Mott transition is still of the usual kind, the magnetic-field-induced MIT falls into a different universality class as there is no field-induced localization of quasiparticles. In the case of a power-law singularity in the DOS at the Fermi level, the power-law singularity persists in the presence of interaction, albeit with a different exponent, and the effective impurity model in the DMFT turns out to be a pseudogap Anderson impurity model with a hybridization function which vanishes at the Fermi level. The system is then a generalized Fermi liquid. At finite doping, regular Fermi-liquid behavior is recovered.

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  • Received 5 August 2009

DOI:https://doi.org/10.1103/PhysRevB.80.245112

©2009 American Physical Society

Authors & Affiliations

Rok Žitko1, Janez Bonča2,1, and Thomas Pruschke3,4

  • 1Jožef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia
  • 2Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
  • 3Institute for Theoretical Physics, University of Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany
  • 4Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem, Israel

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Issue

Vol. 80, Iss. 24 — 15 December 2009

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