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

TL;DR

This study uses DMFT to analyze how Van Hove singularities in the density of states affect the electronic properties and phase transitions of the Hubbard model in different lattice geometries.

Contribution

It reveals how singularities in the DOS influence the Mott transition and magnetic-field-induced transitions, providing new insights into the interplay between lattice geometry and electron correlations.

Findings

Square-root singularities are smoothed out by correlations in 3D lattices.

Logarithmic singularities at the Fermi level persist and affect the Mott transition in 2D lattices.

Power-law singularities remain with modified exponents, leading to a pseudo-gap Anderson impurity model.

Abstract

Using the dynamical mean-field theory (DMFT) we study the paramagnetic phase of the Hubbard model with the density of states (DOS) corresponding to the three-dimensional cubic lattice and the two-dimensional 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 pseudo-gap 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.