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arXiv:2503.09529

Two distinct quantum critical behaviors in the doped two-dimensional periodic Anderson model

Motoharu Kitatani, Thomas Schäfer, A. A. Katanin, A. Toschi, Karsten Held

Published Mar 12, 2025• 0 citations
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Abstract

We study quantum criticality in the doped two-dimensional periodic Anderson model with the hybridization acting as a tuning parameter. Employing the dynamical vertex approximation we find two distinct quantum critical behaviors. One is a quantum critical point between the antiferromagnetically ordered and the Kondo state, both metallic with itinerant $f$ electrons. Here, we obtained the critical exponent $γ\approx 1$ for the temperature dependence of the antiferromagnetic susceptibility. We observe a \emph{second} quantum critical behavior with $γ=2$ above the continuing zero-temperature magnetic order, at a quantum critical point where the $f$ electrons turn from localized to itinerant.

DOI
10.48550/arxiv.2503.09529

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We study the phase diagram and quantum critical region of one of the fundamental models for electronic correlations: the periodic Anderson model. Employing the recently developed dynamical vertex approximation, we find a phase transition between a zero-temperature antiferromagnetic insulator and a Kondo insulator. In the quantum critical region, we determine a critical exponent γ=2 for the antiferromagnetic susceptibility. At higher temperatures, we have free spins with γ=1 instead, whereas at lower temperatures, there is an even stronger increase and suppression of the susceptibility below and above the quantum critical point, respectively.
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We obtain the phase diagram and thermodynamic behavior of the Kondo necklace model for arbitrary dimensions ddd using a representation for the localized and conduction electrons in terms of local Kondo singlet and triplet operators. A decoupling scheme on the double time Green's functions yields the dispersion relation for the excitations of the system. We show that in $d\ensuremath{\geqslant}3$, there is an antiferromagnetically ordered state at finite temperatures terminating at a quantum critical point (QCP). In two dimensions, long-range magnetic order occurs only at T=0T=0T=0. The line of N\'eel transitions for d>2d>2d>2 varies with the distance to the quantum critical point QCP $\ensuremath{\mid}g\ensuremath{\mid}$ as ${T}_{N}\ensuremath{\propto}{\ensuremath{\mid}g\ensuremath{\mid}}^{\ensuremath{\psi}}$, where the shift exponent $\ensuremath{\psi}=1∕(d\ensuremath{-}1)$. In the paramagnetic side of the phase diagram, the spin gap behaves as $\ensuremath{\Delta}\ensuremath{\approx}\sqrt{\ensuremath{\mid}g\ensuremath{\mid}}$ for $d\ensuremath{\geqslant}3$, consistent with the value z=1z=1z=1 found for the dynamical critical exponent. We also find in this region a power law temperature dependence in the specific heat for ${k}_{B}T⪢\ensuremath{\Delta}$ and along the non-Fermi-liquid trajectory. For ${k}_{B}T⪡\ensuremath{\Delta}$, in the so-called Kondo spin liquid phase, the thermodynamic behavior is dominated by an exponential temperature dependence.
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