Thermodynamic quantum critical behavior of the Kondo necklace model

Abstract

We obtain the phase diagram and thermodynamic behavior of the Kondo necklace model for arbitrary dimensions $d$ 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 $d\ge 3$ there is an antiferromagnetically ordered state at finite temperatures terminating at a quantum critical point (QCP). In 2-d, long range magnetic order occurs only at T=0. The line of Neel transitions for $d>2$ varies with the distance to the quantum critical point QCP $|g|$ as, $T_N\propto |g{|}^{\psi }$ where the shift exponent $\psi =1/(d-1)$. In the paramagnetic side of the phase diagram, the spin gap behaves as $\Delta \approx \sqrt{|g|}$ for $d\ge 3$ consistent with the value $z=1$ found for the dynamical critical exponent. We also find in this region a power law temperature dependence in the specific heat for $k_{B}T\gg \Delta$ and along the non-Fermi liquid trajectory. For $k_{B}T\ll \Delta$, in the so-called Kondo spin liquid phase, the thermodynamic behavior is dominated by an exponential temperature dependence.

arXiv commentSubmitted to PRB

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Cited by in corpus (4)

• Bose-Einstein condensation in antiferromagnets close to the saturation field
• Thermodynamic quantum crtical behavior in the anisotropic Kondo necklace model
• s- and d-wave superconductivity in a two-band model
• Kondo spin liquid in Kondo necklace model: Classical disordered phase versus symmetry-protected topological state