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

TL;DR

This paper investigates quantum phase transitions in the Kondo-necklace model using perturbative continuous unitary transformations, revealing critical points, entanglement properties, and dimensional crossover effects.

Contribution

It applies a perturbative method to predict quantum critical points and analyzes entanglement, providing new insights into the model's phase transitions across dimensions.

Findings

Predicts quantum critical points where the energy gap vanishes.

Shows absence of singularities in concurrence derivatives, indicating multipartite entanglement.

Analyzes dimensional crossover from 1D to 2D via ladder structures.

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.