Thermodynamic quantum crtical behavior in the anisotropic Kondo necklace model

TL;DR

This paper investigates the thermodynamic quantum critical behavior of the anisotropic Kondo necklace model across different dimensions, revealing how anisotropy and temperature influence phase transitions and critical exponents.

Contribution

It provides a detailed analysis of the anisotropic Kondo necklace model using the bond-operator method, including phase transition lines, critical exponents, and specific heat behavior at quantum critical points.

Findings

Spin gap exponent $ u z oughly 0.5$ in 3D at zero temperature.

Neel transition line varies with anisotropy and distance to QCP as $T_N o |g|^{rac{1}{d-1}}$ for $d>2$.

Specific heat follows a $T^d$ power law at the quantum critical trajectory.

Abstract

The Ising-like anisotropy parameter $\delta$ in the Kondo necklace model is analyzed using the bond-operator method at zero and finite temperatures for arbitrary $d$ dimensions. A decoupling scheme on the double time Green's functions is used to find the dispersion relation for the excitations of the system. At zero temperature and in the paramagnetic side of the phase diagram, we determine the spin gap exponent $\nu z\approx0.5$ in three dimensions and anisotropy between $0\leq\delta\leq1$, a result consistent with the dynamic exponent $z=1$ for the Gaussian character of the bond-operator treatment. At low but finite temperatures, in the antiferromagnetic phase, the line of Neel transitions is calculated for $\delta\ll1$ and $\delta\approx1$. For $d>2$ it is only re-normalized by the anisotropy parameter and varies with the distance to the quantum critical point QCP $|g|$ as, $T_N \propto |g|^{\psi}$ where the shift exponent $\psi=1/(d-1)$. Nevertheless, in two dimensions, long range magnetic order occurs only at T=0 for any $\delta$. In the paramagnetic phase, we find a power law temperature dependence on the specific heat at the \textit{quantum liquid trajectory} $J/t=(J/t)_{c}$, $T\to0$. It behaves as $C_{V}\propto T^{d}$ for $\delta\leq 1$ and $\delta\approx1$, in concordance with the scaling theory for $z=1$.