Thermodynamic quantum critical behavior of the anisotropic Kondo necklace model

Abstract

a b s t r a c tThe Ising-like anisotropy parameter d 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 nz % 0:5 in three dimensions and anisotropy between 0pdp1, a result consistent with the dynamic exponent z ¼ 1 for the Gaussian character of the bond-operator treatment. On the other hand, in the antiferromagnetic phase at low but finite temperatures, the line of Neel transitions is calculated for d51. For d42 it is only re-normalized by the anisotropy parameter and varies with the distance to the quantum critical point (QCP) jgj as, T N / jgj c where the shift exponent c ¼ 1=ðd À 1Þ. Nevertheless, in two dimensions, a long-range magnetic order occurs only at T ¼ 0 for any d51. In the paramagnetic phase, we also find a power law temperature dependence on the specific heat at the quantum critical trajectory J=t ¼ ðJ=tÞ c , T ! 0. It behaves as C V / T d for dp1 and % 1, in concordance with the scaling theory for z ¼ 1.

Behavior of the Quantum Critical Point and the Fermi-Liquid Domain in the Heavy Fermion Superconductor CeCoIn5 Studied by Resistivity

“…Conversely, a value of z = 1 is expected in a scenario where the f-electron do not form bands. 27) However, a main difficulty might be that the standard scenario, which does not consider polarisation of the bands under field, is simply not applicable to a field induced 11/17 QCP. Experimentally, the mechanism driving the destruction of the AFM order under field, without any kind of metamagnetic transition is also unclear.…”

Gap formation and phase transition of the anisotropic Kondo necklace model: Density matrix renormalization group analysis

“…This parameter takes values from =0 ͑original Kondo necklace͒ to =1 ͑full anisotropic case͒. Different results for the quantum critical behavior of this model ͑in one dimension, at zero temperature͒ have been obtained: using a real-space renormalization group 17 it was determined that for Ͼ 0.58, there was a phase transition at a finite J / t, and that for Ͻ 0.58, the system was in the Kondo singlet phase for all nonzero values of J / t. Using spin wave theory and a numerical Lanczos method for systems up to 24 sites, 18 it was seen that there was always a phase transition for Ͼ 0, and with the bondoperator method, 19 no transition at finite J / t for any anisotropy was found.…”

Quantum critical behavior of the Kondo necklace model with aperiodic exchange modulation

“…On the other hand, at higher dimensions, it is found that the model presents a quantum critical point (QCP) where the nonmagnetic gapped phase goes to zero and at the same time appears a magnetic gapless phase [13][14][15][16]. Then, the KNM was used for studying the effect of magnetic field [17], thermal and magnetic entanglement [18], dimensional crossover [19,20], and anisotropy [21][22][23] in the heavy fermion compounds. Disorder was also considered in the one dimensional KNM, and all seems to indicate that it is an essential ingredient in the study of the heavy fermions materials [24,26].…”