Non-Fermi liquid signatures in the Hubbard Model due to van Hove singularities

TL;DR

This paper investigates how van Hove singularities near the Fermi level induce non-Fermi liquid behavior in the Hubbard model, revealing anomalous self-energy and transport properties relevant to high-temperature superconductors.

Contribution

It demonstrates the emergence of non-Fermi liquid signatures due to van Hove singularities within the Hubbard model using dynamical mean-field theory, highlighting their impact on low-temperature behavior.

Findings

An unusual maximum in the imaginary part of the self-energy near the Fermi level.

Transition from Fermi liquid to non-Fermi liquid resistivity behavior with doping.

Persistence of anomalous energy dependence of self-energy at zero temperature.

Abstract

When a van-Hove singularity is located in the vicinity of the Fermi level, the electronic scattering rate acquires a non-analytic contribution. This invalidates basic assumptions of Fermi liquid theory and within perturbative treatments leads to a non-Fermi liquid self-energy and transport properties.Such anomalies are shown to also occur in the strongly correlated metallic state. We consider the Hubbard model on a two-dimensional square lattice with nearest and next-nearest neighbor hopping within the single-site dynamical mean-field theory. At temperatures on the order of the low-energy scale $T_0$ an unusual maximum emerges in the imaginary part of the self-energy which is renormalized towards the Fermi level for finite doping. At zero temperature this double-well structure is suppressed, but an anomalous energy dependence of the self-energy remains. For the frustrated Hubbard model on the square lattice with next-nearest neighbor hopping, the presence of the van Hove singularity changes the asymptotic low temperature behavior of the resistivity from a Fermi liquid to non-Fermi liquid dependency as function of doping. The results of this work are discussed regarding their relevance for high-temperature cuprate superconductors.