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arXiv:2307.15680

Pseudogap Behavior in the Local Spinon Spectrum of Power-Law Diverging Multichannel Kondo Model

Zuodong Yu, Danqing Hu, Jiangfan Wang, Xinloong Han

Published Jul 28, 2023• 0 citations
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Abstract

Motivated by the emergence of higher-order van Hove singularities (VHS) with power-law divergent density of states (DOS) ($ρ_c(ω)=ρ_0/|ω|^{r}$, $0

DOI
10.48550/arxiv.2307.15680

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Motivated by the emergence of higher-order van Hove singularities (VHS) with power-law divergent density of states (DOS) (ρc(ω)=ρ0/∣ω∣rρ_c(ω)=ρ_0/|ω|^{r}ρc​(ω)=ρ0​/∣ω∣r, $0
Motivated by the emergence of higher-order van Hove singularities (VHS) with power-law divergent density of states (DOS) $({\ensuremath{\rho}}_{c}(\ensuremath{\omega})={\ensuremath{\rho}}_{0}/{|\ensuremath{\omega}|}^{r}, 0<r<1)$ in materials, we investigate a multichannel Kondo model involving conduction electrons near the higher-order van Hove filling, termed power-law diverging multichannel Kondo model. This model considers MMM channel and NNN spin degrees of freedom. Employing a renormalization group analysis and dynamical large-NNN approach, our results reveal the emergence of a pseudogap behavior in the spectral properties of the local impurity at the overscreened fixed point. We precisely determine the conditions under which the pseudogap behavior occurs, either by tuning the exponent rrr or the ratio $\ensuremath{\kappa}=M/N$ to values such as r∗{r}^{*}r∗ or ${\ensuremath{\kappa}}^{*}$. This pseudogap phase of spinon exhibits distinct physical properties that could have an impact on the properties of real systems. The results of this study provide novel insights into the pseudogap behaviors in strongly correlated systems and offer a playground to study the interplay between higher-order van Hove singularities and multichannel Kondo physics.
Controlling the ordered phases of correlated electron systems remains a central challenge in quantum materials design. Divergences in the electronic density of states, known as Van Hove singularities (VHSs), are one obvious route to such control. It is clear from recent work that the exact functional form of these divergences can profoundly affect which phases are realized; a full picture, however, remains elusive. In this work, we use both the hot-spot parquet renormalization group and the truncated-unity functional renormalization group to theoretically study the emergent correlated states of a two-dimensional square-lattice Hubbard model with VHSs at or near the Fermi level. By varying a single hopping parameter, t3t_3t3​, we are able to change the strength of the VHS divergence in the density of states from logarithmic (for t3<t3ct_3 < t_{3c}t3​<t3c​) to power-law (for t3=t3ct_3 = t_{3c}t3​=t3c​). Further increase of t3t_3t3​ (t3>t3ct_3 > t_{3c}t3​>t3c​) causes each original Van Hove point to split into two, both of the conventional logarithmic type. We show that which of these regimes we are in strongly influences the predicted ordered states. We also study the dependence on doping, and find that the ferromagnetic state that occurs at Van Hove filling in these models is unstable to very small shifts in the Fermi level, often giving way to distinct ordered states depending on whether the model is electron- or hole-doped. These results highlight the importance of tuning VHS properties to control ordered states in correlated materials, and offer design rules to engineer these phases in novel systems.
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.