Quantum criticality and first-order transitions in the extended periodic Anderson model

TL;DR

This paper studies the extended periodic Anderson model revealing quantum critical points, first-order transitions, and valence skipping phenomena driven by Coulomb interactions, using multiple theoretical approaches.

Contribution

It introduces a comprehensive analysis of the model with $d$-$f$ Coulomb interaction, identifying critical points and phase transitions not previously characterized.

Findings

Identification of two quantum critical points with diverging valence susceptibility.

Discovery of first-order transitions bounding the Kondo regime at large $U_{df}$.

Observation of valence skipping at very high $U_{df}$ values.

Abstract

We investigate the behavior of the periodic Anderson model in the presence of $d$-$f$ Coulomb interaction ($U_{df}$) using mean-field theory, variational calculation, and exact diagonalization of finite chains. The variational approach based on the Gutzwiller trial wave function gives a critical value of $U_{df}$ and two quantum critical points (QCPs), where the valence susceptibility diverges. We derive the critical exponent for the valence susceptibility and investigate how the position of the QCP depends on the other parameters of the Hamiltonian. For larger values of $U_{df}$, the Kondo regime is bounded by two first-order transitions. These first-order transitions merge into a triple point at a certain value of $U_{df}$. For even larger $U_{df}$ valence skipping occurs. Although the other methods do not give a critical point, they support this scenario.