Quantum phase transitions in the Kondo-necklace model: perturbative continuous unitary transformation approach

Abstract

The Kondo-necklace model can describe magnetic low-energy limit of strongly correlated heavy fermion materials. There exist multiple energy scales in this model corresponding to each phase of the system. Here, we study quantum phase transition between the Kondo-singlet phase and the antiferromagnetic long-range ordered phase, and show the effect of anisotropies in terms of quantum information properties and vanishing energy gap. We employ the "perturbative continuous unitary transformations" approach to calculate the energy gap and spin-spin correlations for the model in the thermodynamic limit of one, two, and three spatial dimensions as well as for spin ladders. In particular, we show that the method, although being perturbative, can predict the expected quantum critical point, where the gap of low-energy spectrum vanishes, which is in good agreement with results of other numerical and Green's function analyses. In addition, we employ concurrence, a bipartite entanglement measure, to study the criticality of the model. Absence of singularities in the derivative of concurrence in two and three dimensions in the Kondo-necklace model shows that this model features multipartite entanglement. We also discuss crossover from the one-dimensional to the two-dimensional model via the ladder structure.

Tomonaga–Luttinger Spin Liquid and Kosterlitz–Thouless Transition in the Spin-1/2 Branched Chains: The Study of Topological Phase Transition

“…Motivated by novel, highly correlated low-dimensional systems, V. O. Cheranovskii et al studied the magnetization process of a series of spin-1/2 chains with different types of intra-chain interactions at low temperatures [46]. The Kondo-necklace models with similar spin structure to the branched chains were considered, and some important results for their ground-state phase transition have been reported [47,48].…”

Electric and Thermoelectric Properties of Cu₁₂Sb₄S₁₃ Tetrahedrite with Impurities

“…In addition, several studies performed on band structure engineering to improve Seebeck coefficient and electric conductivity and implementing nanostructure technology for decreasing the lattice thermal 20 conductivity [4,5]. There has been some research on the effect of Kondo correlations on the thermopower [6,7,8,9,10,11,12].…”