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ANALYSIS THE ENTANGLEMENT IN THE ONE DIMENSIONAL KONDO NECKLACE MODEL

Somayeh Gholami Matehkolaee

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

In this paper, at first we review the history of Kondo models exactly. Then we investigate quantum entanglement in the one-dimensional Kondo Necklace model. In calculations we have got each of the matrices according to Hamiltonian section. These result shows that the ground state are included in two up and down spins. Keywords: Quantum entanglement- Kondo Necklace model- Spin chain.

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In this paper, at first we review the history of Kondo models exactly. Then we investigate quantum entanglement in the one-dimensional Kondo Necklace model. In calculations we have got each of the matrices according to Hamiltonian section. These result shows that the ground state are included in two up and down spins. Keywords: Quantum entanglement- Kondo Necklace model- Spin chain.
We study the entanglement in the one-dimensional Kondo necklace model with exact diagonalization, calculating the concurrence as a function of the Kondo coupling J and an anisotropy η in the interaction between conduction spins, and we review some results previously obtained in the limiting cases η = 0 and 1. We observe that as J increases, localized and conduction spins get more entangled, while neighboring conduction spins diminish their concurrence; localized spins require a minimum concurrence between conduction spins to be entangled. The anisotropy η diminishes the entanglement for neighboring spins when it increases, driving the system to the Ising limit η = 1 where conduction spins are not entangled. We observe that the concurrence does not give information about the quantum phase transition in the anisotropic Kondo necklace model (between a Kondo singlet and an antiferromagnetic state), but calculating the von Neumann block entropy with the density matrix renormalization group in a chain of 100 sites for the Ising limit indicates that this quantity is useful for locating the quantum critical point.
We discuss the thermal and magnetic entanglement in the one-dimensional Kondo necklace model. First, we show how the entanglement naturally present at zero temperature is distributed among pairs of spins according to the strength of the two couplings of the chain, namely, the Kondo exchange interaction and the hopping energy. The effect of temperature and the presence of an external magnetic field are then investigated. We also discuss the adjustment of these variables in order to control the entanglement available in the system. In particular, it is indicated that there exists a critical magnetic field above which the entanglement undergoes a sharp variation, leading the ground state to a completely unentangled phase.
"We use the density matrix renormalization group to calculate the von Neumann block entropy in the Kondo necklace model. We have included two anisotropies: η in the exchange interaction between conduction spins, and ∆ in the coupling between localized and conduction spins. Calculating the energy gap for the one-dimensional model at zero temperature, it was obtained that when η > 0, a quantum phase transition between Kondo singlet and antiferomagnetic states for finite couplings occurs, and as ∆ increases the Kondo singlet phase is favoured. Now we observe that the quantum critical points of the model can be identified by a maximum of the von Neumann block entropy, so entanglement measures can be useful for determining the phase diagram of the anisotropic Kondo necklace model."
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.
The magnetization process of one-dimensional Kondo necklace model with next-nearest-neighbor interaction has been studied by the use of exact-diagonalization method. The magnetization plateaus appear at zero ( m =0) and at half ( m =1/2) of the saturation magnetization. The ground state in the absence of a magnetic field is regarded as an aggregate of intra-atomic Kondo singlets. On the other hand, the spin configuration at the 1/2-plateau represents the intra-chain dimer (σ-dimer) phase with broken translational symmetry. The picture for spin configurations in the uniform magnetic fields other than m =0 and 1/2 are also given. We also determined the phase diagram for the ground state of the system in the magnetic field.
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.