Thermodynamic quantum critical behavior of the Kondo necklace model

TL;DR

This paper investigates the thermodynamic and quantum critical behavior of the Kondo necklace model across different dimensions, revealing how magnetic order and spin gaps evolve near quantum critical points.

Contribution

It introduces a new representation and decoupling scheme to analyze the phase diagram and thermodynamics of the Kondo necklace model in arbitrary dimensions.

Findings

Antiferromagnetic order exists at finite T in d≥3, ending at a QCP.

The Neel transition temperature scales as |g|^{1/(d-1)} near the QCP.

Spin gap behaves as sqrt{|g|} in d≥3, indicating a dynamical critical exponent z=1.

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 $d\geq 3$ 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 $k_BT\gg\Delta$ and along the non-Fermi liquid trajectory. For $k_BT \ll\Delta$, in the so-called Kondo spin liquid phase, the thermodynamic behavior is dominated by an exponential temperature dependence.