Emergent Properties of the Periodic Anderson Model: a High-Resolution, Real-Frequency Study of Heavy-Fermion Quantum Criticality

TL;DR

This study uses high-resolution, real-frequency methods to analyze the quantum critical behavior of the periodic Anderson model, revealing detailed Fermi surface evolution, non-Fermi-liquid regimes, and evidence for f-electron fractionalization.

Contribution

It provides a detailed, high-resolution analysis of the quantum critical point in the periodic Anderson model, including Fermi surface reconstruction and fractionalization evidence, using cellular DMFT and NRG.

Findings

Fermi surface volume changes across the QCP

Vanishing quasiparticle weight at the QCP

Emergence of a Luttinger surface indicating f-electron fractionalization

Abstract

We study paramagnetic quantum criticality in the periodic Anderson model (PAM) using cellular dynamical mean-field theory, with the numerical renormalization group (NRG) as an impurity solver. The PAM describes an itinerant $c$ band hybridizing with a localized $f$ band. At $T=0$, it exhibits a hybridization tuned Kondo breakdown quantum critical point (KB-QCP) from a Kondo to an RKKY phase. At the KB-QCP, the $f$ band changes character from itinerant to mainly localized, while the $c$ band remains itinerant. We elucidate its nature in detail by performing a high-resolution, real-frequency study of dynamical quantities. NRG allows us to study the quantum critical non-Fermi-liquid (NFL) regime located between $T_{FL}<T_{NFL}$. Surprisingly, self-consistency is essential to stabilize the NFL and the QCP. The Fermi-liquid (FL) scale $T_{FL}$ decreases towards and vanishes at the QCP. At $T=0$, we find the following properties. The $f$ quasiparticle (QP) weight $Z_f$ decreases continuously as the QCP is approached from either side, vanishing only at the QCP. Therefore, $Z_f$ is nonzero in both the Kondo and the RKKY phase; hence, the FL QP comprise $c$ and $f$ electrons in both phases. The Fermi surface (FS) volumes in the two phases differ. Whereas the large-FS Kondo phase has a usual two-band structure, the small-FS RKKY phase has an unexpected three-band structure. We provide a detailed analysis of quasiparticle properties of both the Kondo and the RKKY phase. The FS reconstruction is accompanied by the appearance of a Luttinger surface (LS) on which the $f$ self-energy diverges. The FS and LS volumes are related to the density by a generalized Luttinger sum rule. We interpret the small FS volume and the emergent LS as evidence for $f$-electron fractionalization in the RKKY phase. Our Hall coefficient and specific heat are in good qualitative agreement with experiment.