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

We study paramagnetic quantum criticality in the periodic Anderson model (PAM) using cellular dynamical mean-field theory (CDMFT), with the numerical renormalization group (NRG) as a cluster impurity solver. The PAM describes itinerant <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>c</a:mi></a:math> electrons hybridizing with a lattice of localized <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>f</c:mi></c:math> electrons. At zero temperature, it exhibits a much-studied quantum phase transition from a Kondo phase to a Ruderman-Kittel-Kasuya-Yosida (RKKY) phase when the hybridization is decreased through a so-called Kondo breakdown quantum critical point (KB QCP). There, Kondo screening of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>f</e:mi></e:math> spins by <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>c</g:mi></g:math> electrons breaks down, so that <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>f</i:mi></i:math> excitations change their character from somewhat itinerant to mainly localized, while <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>c</k:mi></k:math> excitations remain itinerant. Building on , which interpreted the KB transition as an orbital-selective Mott transition, we here elucidate its nature in great detail by performing a high-resolution, real-frequency study of various dynamical quantities (susceptibilities, self-energies, and spectral functions). NRG allows us to study the quantum critical regime governed by the QCP and located between two temperature scales, <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>T</m:mi><m:mi>FL</m:mi></m:msub><m:mo>&lt;</m:mo><m:msub><m:mi>T</m:mi><m:mi>NFL</m:mi></m:msub></m:math>. In this regime, we find fingerprints of non-Fermi-liquid (NFL) behavior in several dynamical susceptibilities. Surprisingly, CDMFT self-consistency is essential to stabilize the QCP and the NFL regime. The Fermi-liquid (FL) scale <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi>T</o:mi><o:mi>FL</o:mi></o:msub></o:math> decreases toward and vanishes at the KB QCP; at temperatures below <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi>T</q:mi><q:mi>FL</q:mi></q:msub></q:math>, FL behavior emerges. At <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>T</s:mi><s:mo>=</s:mo><s:mn>0</s:mn></s:math>, we find the following properties. The KB transition is continuous. The <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>f</u:mi></u:math> quasiparticle weight decreases continuously as the transition is approached from either side, vanishing only at the KB QCP. Therefore, the quasiparticle weight of the <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>f</w:mi></w:math> band is nonzero not only in the Kondo phase, but also in the RKKY phase; hence, the FL quasiparticles comprise <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi>c</y:mi></y:math> <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi>f</ab:mi></ab:math> electrons in both phases. The Fermi surface (FS) volumes in the two phases differ, implying a FS reconstruction at the KB QCP. Whereas the large-FS Kondo phase has a two-band structure as expected, the small-FS RKKY phase unexpectedly has a three-band structure. We provide a detailed analysis of quasiparticle properties of both the Kondo and, for the first time, also the RKKY phase and uncover their differences. The FS reconstruction is accompanied by the appearance of a Luttinger surface on which the <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi>f</cb:mi></cb:math> self-energy diverges. The volumes of the Luttinger and Fermi surfaces are related to the charge density by a generalized Luttinger sum rule. We interpret the small FS volume and the emergent Luttinger surface as evidence for <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mi>f</eb:mi></eb:math>-electron fractionalization in the RKKY phase. Finally, we compute the temperature dependence of the Hall coefficient and the specific heat, finding good qualitative agreement with experiments. Published by the American Physical Society 2024