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arXiv:1812.03821 · Physical Review Letters

Quantum Criticality in the Two-Dimensional Periodic Anderson Model

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

Published Jun 6, 2019• 34 citations
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Abstract

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.

DOI
10.1103/physrevlett.122.227201

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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.
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 fff electrons. Here, we obtained the critical exponent γ≈1γ\approx 1γ≈1 for the temperature dependence of the antiferromagnetic susceptibility. We observe a \emph{second} quantum critical behavior with γ=2γ=2γ=2 above the continuing zero-temperature magnetic order, at a quantum critical point where the fff electrons turn from localized to itinerant.
Periodic Anderson model is one of the most important models in the field of strongly correlated electrons. With the recent developed numerical method density matrix embedding theory, we study the ground state properties of the periodic Anderson model on a two-dimensional square lattice. We systematically investigate the phase diagram away from half filling. We find three different phases in this region, which are distinguished by the local moment and the spin–spin correlation functions. The phase transition between the two antiferromagnetic phases is of first order. It is the so-called Lifshitz transition accompanied by a reconstruction of the Fermi surface. As the filling is close to half filling, there is no difference between the two antiferromagnetic phases. From the results of the spin–spin correlation, we find that the Kondo singlet is formed even in the antiferromagnetic phase.
We investigate the behavior of the periodic Anderson model in the presence of ddd--fff Coulomb interaction (Udf{U}_{df}Udf​) 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 Udf{U}_{df}Udf​ 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 Udf{U}_{df}Udf​, the Kondo regime is bounded by two first-order transitions. These first-order transitions merge into a triple point at a certain value of Udf{U}_{df}Udf​. For even larger Udf{U}_{df}Udf​ valence skipping occurs. Although the other methods do not give a critical point, they support this scenario.
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.
We investigate quantum phase transitions in the extended periodic Anderson model, which includes electron correlations within and between itinerant and localized bands. We calculate zero and finite temperature properties of the system using the combination of dynamical mean-field theory and the numerical renormalization group. At half filling, a first-order phase transition between a Mott insulating state and a Kondo insulating state occurs in the strong-coupling regime. We furthermore find that a metallic state is stabilized in the weak-coupling regime. This state should be adiabatically connected to the orbital selective Mott state with one orbital-localized and the other itinerant. The effect of hole doping is also addressed.
Motivated by the recent proposal that the Monte Carlo sign problem might be used as an indicator of quantum phase transitions, we simulate the periodic Anderson model at half-filling with a staggered ionic potential using the determinant quantum Monte Carlo (DQMC) approach. We observe a phase transition from a band insulator to a Kondo insulator as the hybridization increases. At finite temperature, an intermediate metallic region emerges between two insulating phases, which is characterized by a pseudogap in the spectral functions near the boundary of the intermediate region and a quasiparticle peak in the middle. The latter coincides with a crossing point of the fff-electron occupation on different sublattices as well as the maximum antiferromagnetic (AFM) correlations. The metallic region extrapolates to a single quantum critical point at zero temperature, which may result in exotic quasiparticle excitations associated with the emergent metallic state. The Monte Carlo sign problem is found to be most pronounced in the quantum critical region, implying a close connection between the two phenomena. Our results are qualitatively supported by the Hartree-Fock (HF) mean-field calculations. Our work reveals interesting physics in inhomogeneous Kondo lattice systems that may be worthwhile of more investigations in the future.